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  <entry>
    <title>串行进位加法器设计/Ripple-Carry Adder</title>
    <link href="/2021/10/08/RippleCarryAdder/"/>
    <url>/2021/10/08/RippleCarryAdder/</url>
    
    <content type="html"><![CDATA[<h1>串行进位加法器设计/Ripple-Carry Adder</h1><h2 id="串行-行波进位-串行-行波进位加法器">串行/行波进位 &amp; 串行/行波进位加法器</h2><p>回顾一位 <strong>FA</strong> （全加器）的设计，不难看到 <strong>FA</strong> 同时考虑了前一位的进位<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">C_{i - 1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.891661em;vertical-align:-0.208331em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span></span></span>和本位计算结果产生的进位<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">C_{i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>。<br>容易联想到将前一位产生的进位<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mrow><mo stretchy="false">(</mo><mi>o</mi><mi>u</mi><mi>t</mi><msub><mo stretchy="false">)</mo><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></msub></mrow><annotation encoding="application/x-tex">C_{(out)_{i - 1}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.03853em;vertical-align:-0.3551999999999999em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.34480000000000005em;"><span style="top:-2.5198em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">t</span><span class="mclose mtight"><span class="mclose mtight">)</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32808571428571426em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.20252142857142857em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3551999999999999em;"><span></span></span></span></span></span></span></span></span></span>输出到下一个 <strong>FA</strong> 的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msub><mo stretchy="false">)</mo><mi>i</mi></msub></mrow></msub></mrow><annotation encoding="application/x-tex">C_{(in)_{i}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.03853em;vertical-align:-0.3551999999999999em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.34480000000000005em;"><span style="top:-2.5198em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span><span class="mclose mtight"><span class="mclose mtight">)</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3551999999999999em;"><span></span></span></span></span></span></span></span></span></span>，串行地联系每位间的进位关系，电路如<a href="#RCAConnect"><strong><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>图</mtext><mn>1.1</mn></mrow><annotation encoding="application/x-tex">图1.1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">图</span><span class="mord">1</span><span class="mord">.</span><span class="mord">1</span></span></span></span></strong></a>所示<br><span id="RCAConnect" display="none"></span><br><img src="/2021/10/08/RippleCarryAdder/RippleCarryAdderConnect.png" alt title="串行进位的 FA 连接方式"><br><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mo stretchy="false">(</mo><mtext>图</mtext><mn>1.1</mn><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{gathered}    (图1.1)\end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5000000000000002em;vertical-align:-0.5000000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1em;"><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord cjk_fallback">图</span><span class="mord">1</span><span class="mord">.</span><span class="mord">1</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5000000000000002em;"><span></span></span></span></span></span></span></span></span></span></span></p><p>第<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi><mo stretchy="false">(</mo><mi>i</mi><mo>≥</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">i(i \ge 1)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault">i</span><span class="mopen">(</span><span class="mord mathdefault">i</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span></span></span></span>位 <strong>FA</strong> 的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><mo stretchy="false">)</mo></mrow></msub></mrow><annotation encoding="application/x-tex">C_{(in)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.03853em;vertical-align:-0.3551999999999999em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.34480000000000005em;"><span style="top:-2.5198em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3551999999999999em;"><span></span></span></span></span></span></span></span></span></span>通过从第<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">i - 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.74285em;vertical-align:-0.08333em;"></span><span class="mord mathdefault">i</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span>个 <strong>FA</strong> 的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mrow><mi>o</mi><mi>u</mi><mi>t</mi></mrow></msub></mrow><annotation encoding="application/x-tex">C_{out}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">t</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>获得进位的方式，叫做<strong>串行/行波进位</strong>，像这样得到加法器叫<strong>串行进位加法器</strong>，或者叫<strong>行波进位加法器(RCA)</strong>。串行连接4个 <strong>FA</strong> 可以组成一个4位加法器，可以进行两个4位二进制数的加法运算。电路如<a href="#RCA4"><strong><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>图</mtext><mn>1.2</mn></mrow><annotation encoding="application/x-tex">图1.2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">图</span><span class="mord">1</span><span class="mord">.</span><span class="mord">2</span></span></span></span></strong></a>所示<br><span id="RCA4" display="none"></span><br><img src="/2021/10/08/RippleCarryAdder/4BitRippleCarryAdder.png" alt title="串行进位的4位二进制数加法器"><br><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mo stretchy="false">(</mo><mtext>图</mtext><mn>1.2</mn><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{gathered}    (图1.2)\end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5000000000000002em;vertical-align:-0.5000000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1em;"><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord cjk_fallback">图</span><span class="mord">1</span><span class="mord">.</span><span class="mord">2</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5000000000000002em;"><span></span></span></span></span></span></span></span></span></span></span></p><p>如法炮制，将一个4位 <strong>RCA</strong> 视为一组，将4组4位 <strong>RCA</strong> 用串行进位的方式连接起来就得到了一个组内串行进位且组间串行进位的16位串行进位加法器。电路如<a href="#RCA16"><strong><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>图</mtext><mn>1.3</mn></mrow><annotation encoding="application/x-tex">图1.3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">图</span><span class="mord">1</span><span class="mord">.</span><span class="mord">3</span></span></span></span></strong></a>所示<br><span id="RCA16" display="none"></span><br><img src="/2021/10/08/RippleCarryAdder/16BitRippleCarryAdder.png" alt title="组内串行进位且组间串行进位的16位二进制数加法器"><br><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mo stretchy="false">(</mo><mtext>图</mtext><mn>1.3</mn><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{gathered}    (图1.3)\end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5000000000000002em;vertical-align:-0.5000000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1em;"><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord cjk_fallback">图</span><span class="mord">1</span><span class="mord">.</span><span class="mord">3</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5000000000000002em;"><span></span></span></span></span></span></span></span></span></span></span></p><p><strong>分析串行进位加法器的不足</strong><br>由于串行连接的方式，使得每位 <strong>FA</strong> 做位加法运算时，需要等待前一位 <strong>FA</strong> 得出进位位<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">C_{i-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.891661em;vertical-align:-0.208331em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span></span></span>的结果才能进行本位的逻辑运算。这使得越高位的 <strong>FA</strong> 等待进位参与本位运算的时间越长，降低了运算效率。</p>]]></content>
    
    
    
    <tags>
      
      <tag>计算机组成原理</tag>
      
      <tag>数字电路</tag>
      
      <tag>CPU</tag>
      
      <tag>逻辑门电路</tag>
      
      <tag>加法器</tag>
      
      <tag>全加器</tag>
      
      <tag>串行进位</tag>
      
      <tag>行波进位</tag>
      
      <tag>串行进位加法器</tag>
      
      <tag>Ripple Carry Adder</tag>
      
    </tags>
    
  </entry>
  
  
  
  <entry>
    <title>全加器/(1 bit)Full Adder</title>
    <link href="/2021/10/08/FullAdder/"/>
    <url>/2021/10/08/FullAdder/</url>
    
    <content type="html"><![CDATA[<h1>全加器/(1 bit)Full Adder</h1><h2 id="1-全加器定义">1. 全加器定义</h2><p><strong>全加器（FA）<strong>是</strong>能够计算低位进位</strong>的二进制逻辑电路元件</p><h2 id="2-全加器真值表及逻辑表达式">2. 全加器真值表及逻辑表达式</h2><table><thead><tr><th style="text-align:left"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">A_{i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></th><th style="text-align:left"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>B</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">B_{i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05017em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></th><th style="text-align:left"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">C_{i-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.891661em;vertical-align:-0.208331em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span></span></span>(Carry)</th><th style="text-align:left"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>S</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">S_{i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>(Sum)</th><th style="text-align:left"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">C_{i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></th></tr></thead><tbody><tr><td style="text-align:left">0</td><td style="text-align:left">0</td><td style="text-align:left">0</td><td style="text-align:left">0</td><td style="text-align:left">0</td></tr><tr><td style="text-align:left">0</td><td style="text-align:left">0</td><td style="text-align:left">1</td><td style="text-align:left">1</td><td style="text-align:left">0</td></tr><tr><td style="text-align:left">0</td><td style="text-align:left">1</td><td style="text-align:left">0</td><td style="text-align:left">1</td><td style="text-align:left">0</td></tr><tr><td style="text-align:left">0</td><td style="text-align:left">1</td><td style="text-align:left">1</td><td style="text-align:left">0</td><td style="text-align:left">1</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">0</td><td style="text-align:left">0</td><td style="text-align:left">1</td><td style="text-align:left">0</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">0</td><td style="text-align:left">1</td><td style="text-align:left">0</td><td style="text-align:left">1</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">1</td><td style="text-align:left">0</td><td style="text-align:left">0</td><td style="text-align:left">1</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">1</td><td style="text-align:left">1</td><td style="text-align:left">1</td><td style="text-align:left">1</td></tr></tbody></table><p>逻辑表达式：</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="right" columnspacing><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><msub><mi>S</mi><mi>i</mi></msub><mo>=</mo><msub><mi>A</mi><mi>i</mi></msub><mo>⨁</mo><msub><mi>B</mi><mi>i</mi></msub><mo>⨁</mo><msub><mi>C</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}    S_{i} = A_{i} \bigoplus B_{i} \bigoplus C_{i-1}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.90001em;vertical-align:-0.7000050000000001em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.200005em;"><span style="top:-3.200005em;"><span class="pstrut" style="height:3.05em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-symbol large-op" style="position:relative;top:-0.000004999999999977245em;">⨁</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05017em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-symbol large-op" style="position:relative;top:-0.000004999999999977245em;">⨁</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7000050000000001em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="right" columnspacing><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><msub><mi>C</mi><mi>i</mi></msub><mo>=</mo><msub><mi>A</mi><mi>i</mi></msub><mo>⋅</mo><msub><mi>B</mi><mi>i</mi></msub><mo>+</mo><msub><mi>C</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>⋅</mo><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><mo>+</mo><msub><mi>B</mi><mi>i</mi></msub><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}    C_{i} = A_{i} \cdot B_{i} + C_{i-1} \cdot (A_{i} + B_{i})\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5000000000000002em;vertical-align:-0.5000000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1em;"><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05017em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05017em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5000000000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p>或</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="right" columnspacing><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><msub><mi>C</mi><mi>i</mi></msub><mo>=</mo><msub><mi>A</mi><mi>i</mi></msub><mo>⋅</mo><msub><mi>B</mi><mi>i</mi></msub><mo>+</mo><msub><mi>C</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>⋅</mo><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><mo>⨁</mo><msub><mi>B</mi><mi>i</mi></msub><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}    C_{i} = A_{i} \cdot B_{i} + C_{i-1} \cdot (A_{i} \bigoplus B_{i})\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.90001em;vertical-align:-0.7000050000000001em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.200005em;"><span style="top:-3.200005em;"><span class="pstrut" style="height:3.05em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05017em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-symbol large-op" style="position:relative;top:-0.000004999999999977245em;">⨁</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05017em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7000050000000001em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><hr><h4 id="补充：真值表的最小逻辑表达式"><strong>补充：真值表的最小逻辑表达式</strong></h4><p><strong>已知逻辑函数F关于多个逻辑变量的真值表，首先找到所有F=1的行，在这些行中，将值为0的若干个逻辑变量取反(使其变为1)，而值为1的变量保持不变，将该行所有变量逻辑与(将所有变量逻辑值相关联)得到该行子逻辑式，然后将这些行逻辑子式逻辑或或，最后化简得到最小逻辑表达式</strong></p><blockquote><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>例如，观察输入</mtext><msub><mi>A</mi><mi>i</mi></msub><mtext>、</mtext><msub><mi>B</mi><mi>i</mi></msub><mtext>、</mtext><msub><mi>C</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mtext>逻辑变量</mtext><msub><mi>X</mi><msub><mi>n</mi><mi>i</mi></msub></msub><mo stretchy="false">)</mo><mtext>与输出</mtext><msub><mi>S</mi><mi>i</mi></msub><mtext>，找到</mtext><msub><mi>S</mi><mi>i</mi></msub><mo>=</mo><mn>1</mn><mtext>的行</mtext></mrow><annotation encoding="application/x-tex">例如，观察输入A_{i}、B_{i}、C_{i-1}(逻辑变量X_{n_{i}})与输出S_{i}，找到S_{i} = 1的行</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0001em;vertical-align:-0.2501em;"></span><span class="mord cjk_fallback">例</span><span class="mord cjk_fallback">如</span><span class="mord cjk_fallback">，</span><span class="mord cjk_fallback">观</span><span class="mord cjk_fallback">察</span><span class="mord cjk_fallback">输</span><span class="mord cjk_fallback">入</span><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord cjk_fallback">、</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05017em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord cjk_fallback">、</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord cjk_fallback">逻</span><span class="mord cjk_fallback">辑</span><span class="mord cjk_fallback">变</span><span class="mord cjk_fallback">量</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139199999999997em;"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord cjk_fallback">与</span><span class="mord cjk_fallback">输</span><span class="mord cjk_fallback">出</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord cjk_fallback">，</span><span class="mord cjk_fallback">找</span><span class="mord cjk_fallback">到</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord cjk_fallback">的</span><span class="mord cjk_fallback">行</span></span></span></span></p><table><thead><tr><th style="text-align:left"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">A_{i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></th><th style="text-align:left"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>B</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">B_{i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05017em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></th><th style="text-align:left"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">C_{i-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.891661em;vertical-align:-0.208331em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span></span></span></th><th style="text-align:left"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>S</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">S_{i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></th></tr></thead><tbody><tr><td style="text-align:left">0</td><td style="text-align:left">0</td><td style="text-align:left">1</td><td style="text-align:left">1</td></tr><tr><td style="text-align:left">0</td><td style="text-align:left">1</td><td style="text-align:left">0</td><td style="text-align:left">1</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">0</td><td style="text-align:left">0</td><td style="text-align:left">1</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">1</td><td style="text-align:left">1</td><td style="text-align:left">1</td></tr></tbody></table><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>即</mtext><msub><mi>S</mi><mi>i</mi></msub><mo>=</mo><mo stretchy="false">(</mo><mover accent="true"><msub><mi>A</mi><mi>i</mi></msub><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mover accent="true"><msub><mi>B</mi><mi>i</mi></msub><mo stretchy="true">‾</mo></mover><mo>⋅</mo><msub><mi>C</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><mover accent="true"><msub><mi>A</mi><mi>i</mi></msub><mo stretchy="true">‾</mo></mover><mo>⋅</mo><msub><mi>B</mi><mi>i</mi></msub><mo>⋅</mo><mover accent="true"><msub><mi>C</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mo stretchy="true">‾</mo></mover><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><mo>⋅</mo><mover accent="true"><msub><mi>B</mi><mi>i</mi></msub><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mover accent="true"><msub><mi>C</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mo stretchy="true">‾</mo></mover><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><mo>⋅</mo><msub><mi>B</mi><mi>i</mi></msub><mo>⋅</mo><msub><mi>C</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">即  S_{i} = (\overline{A_{i}} \cdot \overline{B_{i}} \cdot C_{i-1}) + (\overline{A_{i}} \cdot B_{i} \cdot \overline{C_{i-1}}) + (A_{i} \cdot \overline{B_{i}} \cdot \overline{C_{i-1}}) + (A_{i} \cdot B_{i} \cdot C_{i-1})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord cjk_fallback">即</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.13333em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.03333em;vertical-align:-0.15em;"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05017em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.13333em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05017em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.13333em;vertical-align:-0.25em;"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.03333em;vertical-align:-0.15em;"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05017em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.13333em;vertical-align:-0.25em;"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05017em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></p><p>合并化简，提取<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mo separator="true">,</mo><mover accent="true"><msub><mi>C</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mo stretchy="true">‾</mo></mover><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">C_{i-1},\overline{C_{i-1}},</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.091661em;vertical-align:-0.208331em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span><span class="mpunct">,</span></span></span></span></p><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>即</mtext><msub><mi>S</mi><mi>i</mi></msub><mo>=</mo><msub><mi>C</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>⋅</mo><mo stretchy="false">(</mo><mover accent="true"><msub><mi>A</mi><mi>i</mi></msub><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mover accent="true"><msub><mi>B</mi><mi>i</mi></msub><mo stretchy="true">‾</mo></mover><mo>+</mo><msub><mi>A</mi><mi>i</mi></msub><mo>⋅</mo><msub><mi>B</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>+</mo><mover accent="true"><msub><mi>C</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mo stretchy="false">(</mo><mover accent="true"><msub><mi>A</mi><mi>i</mi></msub><mo stretchy="true">‾</mo></mover><mo>⋅</mo><msub><mi>B</mi><mi>i</mi></msub><mo>+</mo><msub><mi>A</mi><mi>i</mi></msub><mo>⋅</mo><mover accent="true"><msub><mi>B</mi><mi>i</mi></msub><mo stretchy="true">‾</mo></mover><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">即S_{i} = C_{i-1} \cdot (\overline{A_{i}} \cdot \overline{B_{i}} + A_{i} \cdot B_{i}) + \overline{C_{i-1}} \cdot (\overline{A_{i}} \cdot B_{i} + A_{i} \cdot \overline{B_{i}})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord cjk_fallback">即</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.891661em;vertical-align:-0.208331em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.13333em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.03333em;vertical-align:-0.15em;"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05017em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05017em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.091661em;vertical-align:-0.208331em;"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.13333em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05017em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.13333em;vertical-align:-0.25em;"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05017em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span><span class="mclose">)</span></span></span></span></p><p>由<a href="./AOIGate.md#%E5%BC%82%E6%88%96%E9%97%A8%E9%80%BB%E8%BE%91%E8%A1%A8%E8%BE%BE%E5%BC%8F"><strong>异或</strong></a>(<a href="./AOIGate.md#%E8%A1%A5%E5%85%85%EF%BC%9A%E9%80%BB%E8%BE%91%E4%BB%A3%E6%95%B0%E8%BF%90%E7%AE%97%E7%9A%84%E5%9F%BA%E6%9C%AC%E5%85%AC%E5%BC%8F"><em>逻辑代数运算基本公式</em></a>)换算可得<br><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>S</mi><mi>i</mi></msub><mo>=</mo><msub><mi>A</mi><mi>i</mi></msub><mo>⨁</mo><msub><mi>B</mi><mi>i</mi></msub><mo>⨁</mo><msub><mi>C</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mtext>此步换算对于“基础与或非”而言并非化简，但如果</mtext><mi>X</mi><mi>O</mi><mi>R</mi><mtext>被封装，不考虑</mtext><mi>X</mi><mi>O</mi><mi>R</mi><mtext>的实现则此式更便于理解</mtext><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">S_{i} = A_{i} \bigoplus B_{i} \bigoplus C_{i-1}(此步换算对于“基础与或非”而言并非化简，但如果XOR被封装，不考虑XOR的实现则此式更便于理解)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.00001em;vertical-align:-0.25001em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">⨁</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.05017em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">⨁</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord cjk_fallback">此</span><span class="mord cjk_fallback">步</span><span class="mord cjk_fallback">换</span><span class="mord cjk_fallback">算</span><span class="mord cjk_fallback">对</span><span class="mord cjk_fallback">于</span><span class="mord">“</span><span class="mord cjk_fallback">基</span><span class="mord cjk_fallback">础</span><span class="mord cjk_fallback">与</span><span class="mord cjk_fallback">或</span><span class="mord cjk_fallback">非</span><span class="mord">”</span><span class="mord cjk_fallback">而</span><span class="mord cjk_fallback">言</span><span class="mord cjk_fallback">并</span><span class="mord cjk_fallback">非</span><span class="mord cjk_fallback">化</span><span class="mord cjk_fallback">简</span><span class="mord cjk_fallback">，</span><span class="mord cjk_fallback">但</span><span class="mord cjk_fallback">如</span><span class="mord cjk_fallback">果</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mord cjk_fallback">被</span><span class="mord cjk_fallback">封</span><span class="mord cjk_fallback">装</span><span class="mord cjk_fallback">，</span><span class="mord cjk_fallback">不</span><span class="mord cjk_fallback">考</span><span class="mord cjk_fallback">虑</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mord cjk_fallback">的</span><span class="mord cjk_fallback">实</span><span class="mord cjk_fallback">现</span><span class="mord cjk_fallback">则</span><span class="mord cjk_fallback">此</span><span class="mord cjk_fallback">式</span><span class="mord cjk_fallback">更</span><span class="mord cjk_fallback">便</span><span class="mord cjk_fallback">于</span><span class="mord cjk_fallback">理</span><span class="mord cjk_fallback">解</span><span class="mclose">)</span></span></span></span></p></blockquote><hr><h2 id="3-全加器逻辑电路示意图">3. 全加器逻辑电路示意图</h2><blockquote><p><img src="/2021/10/08/FullAdder/FullAdder.png" alt></p></blockquote>]]></content>
    
    
    
    <tags>
      
      <tag>计算机组成原理</tag>
      
      <tag>数字电路</tag>
      
      <tag>CPU</tag>
      
      <tag>逻辑门电路</tag>
      
      <tag>加法器</tag>
      
      <tag>全加器</tag>
      
      <tag>Full Adder</tag>
      
    </tags>
    
  </entry>
  
  
  
  <entry>
    <title>半加器/(1 bit)Half Adder</title>
    <link href="/2021/10/08/HalfAdder/"/>
    <url>/2021/10/08/HalfAdder/</url>
    
    <content type="html"><![CDATA[<h1>半加器/(1 bit)Half Adder</h1><h2 id="1-半加器定义">1. 半加器定义</h2><p>半加器是指<em><strong>对两个输入数据位相加，输出一个结果位和进位，没有进位输入</strong></em>的加法器。 是实现两个一位二进制数的加法运算电路。</p><h2 id="2-半加器真值表及逻辑表达式">2. 半加器真值表及逻辑表达式</h2><table><thead><tr><th style="text-align:left">A</th><th style="text-align:left">B</th><th style="text-align:left">S(Sum)</th><th style="text-align:left">C(Carry)</th></tr></thead><tbody><tr><td style="text-align:left">0</td><td style="text-align:left">0</td><td style="text-align:left">0</td><td style="text-align:left">0</td></tr><tr><td style="text-align:left">0</td><td style="text-align:left">1</td><td style="text-align:left">1</td><td style="text-align:left">0</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">0</td><td style="text-align:left">1</td><td style="text-align:left">0</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">1</td><td style="text-align:left">0</td><td style="text-align:left">1</td></tr></tbody></table><p>其中A、B为输入 , S、C为输出</p><p>联系A、B、S可以看出(A异或B)</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="right" columnspacing><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>S</mi><mo>=</mo><mi>A</mi><mo>⨁</mo><mi>B</mi><mo>=</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mi>B</mi><mo>+</mo><mi>A</mi><mover accent="true"><mi>B</mi><mo stretchy="true">‾</mo></mover></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}    S = A \bigoplus B =\overline{A}B + A\overline{B}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.90001em;vertical-align:-0.7000050000000001em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.200005em;"><span style="top:-3.200005em;"><span class="pstrut" style="height:3.05em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-symbol large-op" style="position:relative;top:-0.000004999999999977245em;">⨁</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7000050000000001em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p>联系A、B、C可以看出(A与B)</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="right" columnspacing><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>C</mi><mo>=</mo><mi>A</mi><mo>×</mo><mi>B</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}    C = A \times B\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5000000000000002em;vertical-align:-0.5000000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1em;"><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5000000000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><h2 id="3-逻辑电路示意图">3. <em>逻辑电路示意图</em></h2><blockquote><p><img src="/2021/10/08/HalfAdder/OneBitHalfAdder.png" alt></p></blockquote>]]></content>
    
    
    
    <tags>
      
      <tag>计算机组成原理</tag>
      
      <tag>数字电路</tag>
      
      <tag>CPU</tag>
      
      <tag>逻辑门电路</tag>
      
      <tag>加法器</tag>
      
      <tag>半加器</tag>
      
      <tag>Half Adder</tag>
      
    </tags>
    
  </entry>
  
  
  
  <entry>
    <title>LogicGateCircuit</title>
    <link href="/2021/10/08/LogicGateCircuit/"/>
    <url>/2021/10/08/LogicGateCircuit/</url>
    
    <content type="html"><![CDATA[<h1>逻辑门电路/LGC</h1><h2 id="基础逻辑电路-与门-或门-非门">基础逻辑电路:与门、或门、非门</h2><ol><li><h3 id="与门-and">与门/AND</h3><ol><li>与门真值表<table><thead><tr><th style="text-align:left">A</th><th style="text-align:left">B</th><th style="text-align:left">S</th></tr></thead><tbody><tr><td style="text-align:left">0</td><td style="text-align:left">0</td><td style="text-align:left">0</td></tr><tr><td style="text-align:left">0</td><td style="text-align:left">1</td><td style="text-align:left">0</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">0</td><td style="text-align:left">0</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">1</td><td style="text-align:left">1</td></tr></tbody></table></li><li>与门逻辑电路示意图<blockquote><p><img src="/2021/10/08/LogicGateCircuit/ANDGate.png" alt></p></blockquote></li></ol></li><li><h3 id="或门-or">或门/OR</h3><ol><li>或门真值表<table><thead><tr><th style="text-align:left">A</th><th style="text-align:left">B</th><th style="text-align:left">S</th></tr></thead><tbody><tr><td style="text-align:left">0</td><td style="text-align:left">0</td><td style="text-align:left">0</td></tr><tr><td style="text-align:left">0</td><td style="text-align:left">1</td><td style="text-align:left">1</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">0</td><td style="text-align:left">1</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">1</td><td style="text-align:left">1</td></tr></tbody></table></li><li>或门逻辑电路示意图<blockquote><p><img src="/2021/10/08/LogicGateCircuit/ORGate.png" alt></p></blockquote></li></ol></li><li><h3 id="非门-not">非门/NOT</h3><ol><li>非门真值表<table><thead><tr><th style="text-align:left">A</th><th style="text-align:left">S</th></tr></thead><tbody><tr><td style="text-align:left">1</td><td style="text-align:left">0</td></tr><tr><td style="text-align:left">0</td><td style="text-align:left">1</td></tr></tbody></table></li><li>非门逻辑电路示意图<blockquote><p><img src="/2021/10/08/LogicGateCircuit/NOTGate.png" alt></p></blockquote></li></ol></li></ol><h2 id="其他常见-逻辑-门电路">其他常见(逻辑)门电路</h2><ol><li><h3 id="与非门">与非门</h3><ol><li>与非门真值表<table><thead><tr><th style="text-align:left">A</th><th style="text-align:left">B</th><th style="text-align:left">S</th></tr></thead><tbody><tr><td style="text-align:left">0</td><td style="text-align:left">0</td><td style="text-align:left">1</td></tr><tr><td style="text-align:left">0</td><td style="text-align:left">1</td><td style="text-align:left">1</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">0</td><td style="text-align:left">1</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">1</td><td style="text-align:left">0</td></tr></tbody></table></li><li>与非门逻辑表达式<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="right" columnspacing><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>S</mi><mo>=</mo><mover accent="true"><mrow><mi>A</mi><mo>⋅</mo><mi>B</mi></mrow><mo stretchy="true">‾</mo></mover><mo>=</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>+</mo><mover accent="true"><mi>B</mi><mo stretchy="true">‾</mo></mover></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}    S = \overline{A\cdot B} = \overline{A} + \overline{B}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.54333em;vertical-align:-0.5216650000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.021665em;"><span style="top:-3.138335em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5216650000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></p></li><li>与非门逻辑电路示意图<blockquote><p><img src="/2021/10/08/LogicGateCircuit/NANDGateI.png" alt><br><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="right" columnspacing><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>O</mi><mi>R</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}            OR        \end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5000000000000002em;vertical-align:-0.5000000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1em;"><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5000000000000002em;"><span></span></span></span></span></span></span></span></span></span></span><br><img src="/2021/10/08/LogicGateCircuit/NANDGateII.png" alt></p></blockquote></li></ol></li><li><h3 id="或非门">或非门</h3><ol><li>或非门真值表<table><thead><tr><th style="text-align:left">A</th><th style="text-align:left">B</th><th style="text-align:left">S</th></tr></thead><tbody><tr><td style="text-align:left">0</td><td style="text-align:left">0</td><td style="text-align:left">1</td></tr><tr><td style="text-align:left">0</td><td style="text-align:left">1</td><td style="text-align:left">0</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">0</td><td style="text-align:left">0</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">1</td><td style="text-align:left">0</td></tr></tbody></table></li><li>或非门逻辑表达式<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="right" columnspacing><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>S</mi><mo>=</mo><mover accent="true"><mrow><mi>A</mi><mo>+</mo><mi>B</mi></mrow><mo stretchy="true">‾</mo></mover><mo>=</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mover accent="true"><mi>B</mi><mo stretchy="true">‾</mo></mover></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}    S = \overline{A + B} = \overline{A} \cdot \overline{B}\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.54333em;vertical-align:-0.5216650000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.021665em;"><span style="top:-3.138335em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.08333em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5216650000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></p></li><li>或非门逻辑电路示意图<blockquote><p><img src="/2021/10/08/LogicGateCircuit/NORGateI.png" alt><br><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="right" columnspacing><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>O</mi><mi>R</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}            OR        \end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5000000000000002em;vertical-align:-0.5000000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1em;"><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5000000000000002em;"><span></span></span></span></span></span></span></span></span></span></span><br><img src="/2021/10/08/LogicGateCircuit/NORGateII.png" alt></p></blockquote></li></ol></li><li><h3 id="异或门">异或门</h3><ol><li>异或门真值表<table><thead><tr><th style="text-align:left">A</th><th style="text-align:left">B</th><th style="text-align:left">S</th></tr></thead><tbody><tr><td style="text-align:left">0</td><td style="text-align:left">0</td><td style="text-align:left">0</td></tr><tr><td style="text-align:left">0</td><td style="text-align:left">1</td><td style="text-align:left">1</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">0</td><td style="text-align:left">1</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">1</td><td style="text-align:left">0</td></tr></tbody></table></li><li>异或门逻辑表达式<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="right" columnspacing><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>S</mi><mo>=</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mi>B</mi><mo>+</mo><mi>A</mi><mo>⋅</mo><mover accent="true"><mi>B</mi><mo stretchy="true">‾</mo></mover><mo>=</mo><mo stretchy="false">(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo stretchy="false">)</mo><mo>⋅</mo><mo stretchy="false">(</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>+</mo><mover accent="true"><mi>B</mi><mo stretchy="true">‾</mo></mover><mo stretchy="false">)</mo><mo>=</mo><mover accent="true"><mrow><mi>A</mi><mo>⨀</mo><mi>B</mi></mrow><mo stretchy="true">‾</mo></mover><mo>=</mo><mi>A</mi><mo>⨁</mo><mi>B</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}    S = \overline{A} \cdot B + A \cdot \overline{B} = (A + B) \cdot (\overline{A} + \overline{B}) = \overline{A \bigodot B} = A \bigoplus B\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.1000100000000006em;vertical-align:-0.8000050000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3000050000000005em;"><span style="top:-3.3000050000000005em;"><span class="pstrut" style="height:3.2500000000000004em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2500000000000004em;"><span style="top:-3.05em;"><span class="pstrut" style="height:3.05em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-symbol large-op" style="position:relative;top:-0.000004999999999977245em;">⨀</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span><span style="top:-4.220000000000001em;"><span class="pstrut" style="height:3.05em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.55001em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-symbol large-op" style="position:relative;top:-0.000004999999999977245em;">⨁</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8000050000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></p></li><li>异或门逻辑电路示意图<blockquote><p><img src="/2021/10/08/LogicGateCircuit/XORGateI.png" alt><br><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="right" columnspacing><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>O</mi><mi>R</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}            OR        \end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5000000000000002em;vertical-align:-0.5000000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1em;"><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5000000000000002em;"><span></span></span></span></span></span></span></span></span></span></span><br><img src="/2021/10/08/LogicGateCircuit/XORGateII.png" alt></p></blockquote></li></ol></li><li><h3 id="同或门">同或门</h3><ol><li>同或门真值表<table><thead><tr><th style="text-align:left">A</th><th style="text-align:left">B</th><th style="text-align:left">S</th></tr></thead><tbody><tr><td style="text-align:left">0</td><td style="text-align:left">0</td><td style="text-align:left">1</td></tr><tr><td style="text-align:left">0</td><td style="text-align:left">1</td><td style="text-align:left">0</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">0</td><td style="text-align:left">0</td></tr><tr><td style="text-align:left">1</td><td style="text-align:left">1</td><td style="text-align:left">1</td></tr></tbody></table></li><li>同或门逻辑表达式<p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="right" columnspacing><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>S</mi><mo>=</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mover accent="true"><mi>B</mi><mo stretchy="true">‾</mo></mover><mo>+</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>=</mo><mo stretchy="false">(</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>+</mo><mi>B</mi><mo stretchy="false">)</mo><mo>⋅</mo><mo stretchy="false">(</mo><mi>A</mi><mo>+</mo><mover accent="true"><mi>B</mi><mo stretchy="true">‾</mo></mover><mo stretchy="false">)</mo><mo>=</mo><mover accent="true"><mrow><mi>A</mi><mo>⨁</mo><mi>B</mi></mrow><mo stretchy="true">‾</mo></mover><mo>=</mo><mi>A</mi><mo>⨀</mo><mi>B</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}    S = \overline{A} \cdot \overline{B} + A \cdot B = (\overline{A} + B) \cdot (A + \overline{B}) = \overline{A \bigoplus B} = A \bigodot B\end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.1000100000000006em;vertical-align:-0.8000050000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3000050000000005em;"><span style="top:-3.3000050000000005em;"><span class="pstrut" style="height:3.2500000000000004em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mopen">(</span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2500000000000004em;"><span style="top:-3.05em;"><span class="pstrut" style="height:3.05em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-symbol large-op" style="position:relative;top:-0.000004999999999977245em;">⨁</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span><span style="top:-4.220000000000001em;"><span class="pstrut" style="height:3.05em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.55001em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-symbol large-op" style="position:relative;top:-0.000004999999999977245em;">⨀</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8000050000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></p></li><li>同或门逻辑电路示意图<blockquote><p><img src="/2021/10/08/LogicGateCircuit/XNORGateI.png" alt><br><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="right" columnspacing><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>O</mi><mi>R</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{aligned}            OR        \end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5000000000000002em;vertical-align:-0.5000000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1em;"><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5000000000000002em;"><span></span></span></span></span></span></span></span></span></span></span><br><img src="/2021/10/08/LogicGateCircuit/XNORGateII.png" alt></p></blockquote></li></ol></li></ol><hr><h3 id="补充：逻辑代数运算的基本公式"><strong>补充：逻辑代数运算的基本公式</strong></h3><ol><li>德·摩根定律(反演律)</li></ol><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="right" columnspacing><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mover accent="true"><mrow><mi>A</mi><mo>⋅</mo><mi>B</mi></mrow><mo stretchy="true">‾</mo></mover><mo>=</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>+</mo><mover accent="true"><mi>B</mi><mo stretchy="true">‾</mo></mover><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>1.1</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mover accent="true"><mrow><mi>A</mi><mo>+</mo><mi>B</mi></mrow><mo stretchy="true">‾</mo></mover><mo>=</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mover accent="true"><mi>B</mi><mo stretchy="true">‾</mo></mover><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>1.2</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{aligned}        \overline{A \cdot B} = \overline{A} + \overline{B} \qquad(式1.1) \\        \overline{A + B} = \overline{A} \cdot \overline{B} \qquad(式1.2)    \end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.08666em;vertical-align:-1.29333em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.79333em;"><span style="top:-3.91em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">1</span><span class="mord">.</span><span class="mord">1</span><span class="mclose">)</span></span></span><span style="top:-2.36667em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.08333em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">1</span><span class="mord">.</span><span class="mord">2</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.29333em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><ol start="2"><li>交换律、结合律与分配律</li></ol><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="right" columnspacing><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>A</mi><mo>+</mo><mi>B</mi><mo>=</mo><mi>B</mi><mo>+</mo><mi>A</mi><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>2.1</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>=</mo><mi>B</mi><mo>⋅</mo><mi>A</mi><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>2.2</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mo stretchy="false">(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo stretchy="false">)</mo><mo>+</mo><mi>C</mi><mo>=</mo><mi>A</mi><mo>+</mo><mo stretchy="false">(</mo><mi>B</mi><mo>+</mo><mi>C</mi><mo stretchy="false">)</mo><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>2.3</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mo stretchy="false">(</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mo stretchy="false">)</mo><mo>⋅</mo><mi>C</mi><mo>=</mo><mi>A</mi><mo>⋅</mo><mo stretchy="false">(</mo><mi>B</mi><mo>⋅</mo><mi>C</mi><mo stretchy="false">)</mo><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>2.4</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>A</mi><mo>⋅</mo><mo stretchy="false">(</mo><mi>B</mi><mo>+</mo><mi>C</mi><mo stretchy="false">)</mo><mo>=</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>+</mo><mi>A</mi><mo>⋅</mo><mi>C</mi><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>2.5</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{aligned}        A + B = B + A \qquad(式2.1) \\        A \cdot B = B \cdot A \qquad(式2.2) \\        (A + B) + C = A + (B + C) \qquad(式2.3) \\        (A \cdot B) \cdot C = A \cdot (B \cdot C) \qquad(式2.4) \\        A \cdot (B + C) = A \cdot B + A \cdot C \qquad(式2.5)    \end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:7.500000000000002em;vertical-align:-3.5000000000000018em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:4em;"><span style="top:-6.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">2</span><span class="mord">.</span><span class="mord">1</span><span class="mclose">)</span></span></span><span style="top:-4.659999999999999em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">2</span><span class="mord">.</span><span class="mord">2</span><span class="mclose">)</span></span></span><span style="top:-3.1599999999999984em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mclose">)</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">2</span><span class="mord">.</span><span class="mord">3</span><span class="mclose">)</span></span></span><span style="top:-1.6599999999999984em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mclose">)</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">2</span><span class="mord">.</span><span class="mord">4</span><span class="mclose">)</span></span></span><span style="top:-0.15999999999999837em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">2</span><span class="mord">.</span><span class="mord">5</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.5000000000000018em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><ol start="3"><li>与或非逻辑推断</li></ol><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="right" columnspacing><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mn>0</mn><mo>⋅</mo><mi>A</mi><mo>=</mo><mn>0</mn><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>3.1</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mn>1</mn><mo>⋅</mo><mi>A</mi><mo>=</mo><mn>1</mn><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>3.2</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>A</mi><mo>⋅</mo><mi>A</mi><mo>=</mo><mi>A</mi><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>3.3</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>A</mi><mo>⋅</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>=</mo><mn>0</mn><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>3.4</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mn>0</mn><mo>+</mo><mi>A</mi><mo>=</mo><mi>A</mi><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>3.5</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mn>1</mn><mo>+</mo><mi>A</mi><mo>=</mo><mn>1</mn><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>3.6</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>A</mi><mo>+</mo><mi>A</mi><mo>=</mo><mi>A</mi><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>3.7</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>A</mi><mo>+</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>=</mo><mn>1</mn><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>3.8</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{aligned}        0 \cdot A = 0 \qquad(式3.1) \\        1 \cdot A = 1 \qquad(式3.2) \\        A \cdot A = A \qquad(式3.3) \\        A \cdot \overline{A} = 0 \qquad(式3.4) \\\\        0 + A = A \qquad(式3.5) \\        1 + A = 1 \qquad(式3.6) \\        A + A = A \qquad(式3.7) \\        A + \overline{A} = 1 \qquad(式3.8)    \end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:13.586660000000002em;vertical-align:-6.54333em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:7.043330000000001em;"><span style="top:-9.203330000000001em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord">0</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">3</span><span class="mord">.</span><span class="mord">1</span><span class="mclose">)</span></span></span><span style="top:-7.703330000000001em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">3</span><span class="mord">.</span><span class="mord">2</span><span class="mclose">)</span></span></span><span style="top:-6.20333em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">3</span><span class="mord">.</span><span class="mord">3</span><span class="mclose">)</span></span></span><span style="top:-4.66em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord">0</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">3</span><span class="mord">.</span><span class="mord">4</span><span class="mclose">)</span></span></span><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-1.6600000000000004em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">3</span><span class="mord">.</span><span class="mord">5</span><span class="mclose">)</span></span></span><span style="top:-0.1600000000000006em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">3</span><span class="mord">.</span><span class="mord">6</span><span class="mclose">)</span></span></span><span style="top:1.339999999999999em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">3</span><span class="mord">.</span><span class="mord">7</span><span class="mclose">)</span></span></span><span style="top:2.88333em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">3</span><span class="mord">.</span><span class="mord">8</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:6.54333em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><ol start="4"><li>其他</li></ol><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>A</mi><mo>⋅</mo><mo stretchy="false">(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mi>A</mi><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>4.1</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{gathered}        A \cdot (A + B) = A \qquad(式4.1) \\    \end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5000000000000002em;vertical-align:-0.5000000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1em;"><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">4</span><span class="mord">.</span><span class="mord">1</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5000000000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>证明</mtext><mo>:</mo><mtext>原式扩写为</mtext><mi>A</mi><mo>⋅</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>+</mo><mi>A</mi><mo>⋅</mo><mo stretchy="false">(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo stretchy="false">)</mo><mo separator="true">,</mo><mtext>提取</mtext><mi>A</mi><mo separator="true">,</mo><mtext>则</mtext><mi>A</mi><mo>⋅</mo><mo stretchy="false">(</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>+</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mi>A</mi><mo>⋅</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mi>A</mi><mo>⋅</mo><mn>1</mn><mo>=</mo><mi>A</mi><mo separator="true">,</mo><mtext>得证</mtext></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{gathered}        证明:原式扩写为A \cdot \overline{A} + A \cdot (A + B),提取A,则A \cdot (\overline{A} + A + B) = A \cdot (1 + B) = A \cdot 1 = A,得证 \\    \end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.54333em;vertical-align:-0.5216650000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.021665em;"><span style="top:-3.138335em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord cjk_fallback">证</span><span class="mord cjk_fallback">明</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">原</span><span class="mord cjk_fallback">式</span><span class="mord cjk_fallback">扩</span><span class="mord cjk_fallback">写</span><span class="mord cjk_fallback">为</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">提</span><span class="mord cjk_fallback">取</span><span class="mord mathdefault">A</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">则</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">得</span><span class="mord cjk_fallback">证</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5216650000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>注解</mtext><mo>:</mo><mtext>在由若干个不定项组成的逻辑与运算的所有项中，只存在一个单逻辑值项时，此单逻辑值具有的强决定性</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{gathered}        注解:在由若干个不定项组成的逻辑与运算的所有项中，只存在一个单逻辑值项时，此单逻辑值具有的强决定性 \\\\\\    \end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.500000000000002em;vertical-align:-2.000000000000001em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.5000000000000004em;"><span style="top:-4.66em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord cjk_fallback">注</span><span class="mord cjk_fallback">解</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">在</span><span class="mord cjk_fallback">由</span><span class="mord cjk_fallback">若</span><span class="mord cjk_fallback">干</span><span class="mord cjk_fallback">个</span><span class="mord cjk_fallback">不</span><span class="mord cjk_fallback">定</span><span class="mord cjk_fallback">项</span><span class="mord cjk_fallback">组</span><span class="mord cjk_fallback">成</span><span class="mord cjk_fallback">的</span><span class="mord cjk_fallback">逻</span><span class="mord cjk_fallback">辑</span><span class="mord cjk_fallback">与</span><span class="mord cjk_fallback">运</span><span class="mord cjk_fallback">算</span><span class="mord cjk_fallback">的</span><span class="mord cjk_fallback">所</span><span class="mord cjk_fallback">有</span><span class="mord cjk_fallback">项</span><span class="mord cjk_fallback">中</span><span class="mord cjk_fallback">，</span><span class="mord cjk_fallback">只</span><span class="mord cjk_fallback">存</span><span class="mord cjk_fallback">在</span><span class="mord cjk_fallback">一</span><span class="mord cjk_fallback">个</span><span class="mord cjk_fallback">单</span><span class="mord cjk_fallback">逻</span><span class="mord cjk_fallback">辑</span><span class="mord cjk_fallback">值</span><span class="mord cjk_fallback">项</span><span class="mord cjk_fallback">时</span><span class="mord cjk_fallback">，</span><span class="mord cjk_fallback">此</span><span class="mord cjk_fallback">单</span><span class="mord cjk_fallback">逻</span><span class="mord cjk_fallback">辑</span><span class="mord cjk_fallback">值</span><span class="mord cjk_fallback">具</span><span class="mord cjk_fallback">有</span><span class="mord cjk_fallback">的</span><span class="mord cjk_fallback">强</span><span class="mord cjk_fallback">决</span><span class="mord cjk_fallback">定</span><span class="mord cjk_fallback">性</span></span></span><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-1.6599999999999993em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.000000000000001em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>A</mi><mo>+</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>=</mo><mi>A</mi><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>4.2</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{gathered}        A + A \cdot B = A \qquad(式4.2) \\    \end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5000000000000002em;vertical-align:-0.5000000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1em;"><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">4</span><span class="mord">.</span><span class="mord">2</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5000000000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>证明</mtext><mo>:</mo><mtext>原式扩写为</mtext><mi>A</mi><mo>⋅</mo><mi>A</mi><mo>+</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mo separator="true">,</mo><mtext>提取</mtext><mi>A</mi><mo separator="true">,</mo><mtext>得</mtext><mi>A</mi><mo>⋅</mo><mo stretchy="false">(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo stretchy="false">)</mo><mo separator="true">,</mo><mtext>由式</mtext><mn>4.1</mn><mtext>可知</mtext><mo separator="true">,</mo><mtext>结果为</mtext><mi>A</mi><mo separator="true">,</mo><mtext>得证</mtext></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{gathered}        证明:原式扩写为A \cdot A + A \cdot B,提取A,得A \cdot (A + B), 由式4.1可知,结果为A,得证 \\    \end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5000000000000002em;vertical-align:-0.5000000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1em;"><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord cjk_fallback">证</span><span class="mord cjk_fallback">明</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">原</span><span class="mord cjk_fallback">式</span><span class="mord cjk_fallback">扩</span><span class="mord cjk_fallback">写</span><span class="mord cjk_fallback">为</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">提</span><span class="mord cjk_fallback">取</span><span class="mord mathdefault">A</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">得</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">由</span><span class="mord cjk_fallback">式</span><span class="mord">4</span><span class="mord">.</span><span class="mord">1</span><span class="mord cjk_fallback">可</span><span class="mord cjk_fallback">知</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">结</span><span class="mord cjk_fallback">果</span><span class="mord cjk_fallback">为</span><span class="mord mathdefault">A</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">得</span><span class="mord cjk_fallback">证</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5000000000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>注解</mtext><mo>:</mo><mtext>在由若干个不定项组成的逻辑或运算的所有项中，只存在一个单逻辑值项时，此单逻辑值具有的强决定性</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{gathered}        注解:在由若干个不定项组成的逻辑或运算的所有项中，只存在一个单逻辑值项时，此单逻辑值具有的强决定性 \\\\\\    \end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.500000000000002em;vertical-align:-2.000000000000001em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.5000000000000004em;"><span style="top:-4.66em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord cjk_fallback">注</span><span class="mord cjk_fallback">解</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">在</span><span class="mord cjk_fallback">由</span><span class="mord cjk_fallback">若</span><span class="mord cjk_fallback">干</span><span class="mord cjk_fallback">个</span><span class="mord cjk_fallback">不</span><span class="mord cjk_fallback">定</span><span class="mord cjk_fallback">项</span><span class="mord cjk_fallback">组</span><span class="mord cjk_fallback">成</span><span class="mord cjk_fallback">的</span><span class="mord cjk_fallback">逻</span><span class="mord cjk_fallback">辑</span><span class="mord cjk_fallback">或</span><span class="mord cjk_fallback">运</span><span class="mord cjk_fallback">算</span><span class="mord cjk_fallback">的</span><span class="mord cjk_fallback">所</span><span class="mord cjk_fallback">有</span><span class="mord cjk_fallback">项</span><span class="mord cjk_fallback">中</span><span class="mord cjk_fallback">，</span><span class="mord cjk_fallback">只</span><span class="mord cjk_fallback">存</span><span class="mord cjk_fallback">在</span><span class="mord cjk_fallback">一</span><span class="mord cjk_fallback">个</span><span class="mord cjk_fallback">单</span><span class="mord cjk_fallback">逻</span><span class="mord cjk_fallback">辑</span><span class="mord cjk_fallback">值</span><span class="mord cjk_fallback">项</span><span class="mord cjk_fallback">时</span><span class="mord cjk_fallback">，</span><span class="mord cjk_fallback">此</span><span class="mord cjk_fallback">单</span><span class="mord cjk_fallback">逻</span><span class="mord cjk_fallback">辑</span><span class="mord cjk_fallback">值</span><span class="mord cjk_fallback">具</span><span class="mord cjk_fallback">有</span><span class="mord cjk_fallback">的</span><span class="mord cjk_fallback">强</span><span class="mord cjk_fallback">决</span><span class="mord cjk_fallback">定</span><span class="mord cjk_fallback">性</span></span></span><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-1.6599999999999993em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.000000000000001em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>⋅</mo><mo stretchy="false">(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>4.3</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{gathered}        A \cdot B \cdot (A + B) = A \cdot B \qquad(式4.3) \\    \end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5000000000000002em;vertical-align:-0.5000000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1em;"><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">4</span><span class="mord">.</span><span class="mord">3</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5000000000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>证明</mtext><mo>:</mo><mtext>由分配律得</mtext><mi>A</mi><mo>⋅</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>+</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>⋅</mo><mi>B</mi><mo>=</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>+</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>=</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mo separator="true">,</mo><mtext>得证</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{gathered}        证明:由分配律得A \cdot A \cdot B + A \cdot B \cdot B = A \cdot B + A \cdot B = A \cdot B,得证 \\\\\\    \end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.500000000000002em;vertical-align:-2.000000000000001em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.5000000000000004em;"><span style="top:-4.66em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord cjk_fallback">证</span><span class="mord cjk_fallback">明</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">由</span><span class="mord cjk_fallback">分</span><span class="mord cjk_fallback">配</span><span class="mord cjk_fallback">律</span><span class="mord cjk_fallback">得</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">得</span><span class="mord cjk_fallback">证</span></span></span><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-1.6599999999999993em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.000000000000001em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>+</mo><mo stretchy="false">(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo stretchy="false">)</mo><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>4.4</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{gathered}        A \cdot B + (A + B) = (A + B) \qquad(式4.4) \\    \end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5000000000000002em;vertical-align:-0.5000000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1em;"><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">4</span><span class="mord">.</span><span class="mord">4</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5000000000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>证明</mtext><mo>:</mo><mtext>原式扩写为</mtext><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>+</mo><mi>A</mi><mo>⋅</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo separator="true">,</mo><mtext>提取</mtext><mi>A</mi><mo separator="true">,</mo><mtext>得</mtext><mi>A</mi><mo>⋅</mo><mo stretchy="false">(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo stretchy="false">)</mo><mo>+</mo><mi>B</mi><mo>=</mo><mo stretchy="false">(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo stretchy="false">)</mo><mo separator="true">,</mo><mtext>得证</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{gathered}        证明:原式扩写为A \cdot B + A \cdot A + B,提取A,得A \cdot (A + B) + B = (A + B),得证 \\\\\\    \end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.500000000000002em;vertical-align:-2.000000000000001em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.5000000000000004em;"><span style="top:-4.66em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord cjk_fallback">证</span><span class="mord cjk_fallback">明</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">原</span><span class="mord cjk_fallback">式</span><span class="mord cjk_fallback">扩</span><span class="mord cjk_fallback">写</span><span class="mord cjk_fallback">为</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">提</span><span class="mord cjk_fallback">取</span><span class="mord mathdefault">A</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">得</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">得</span><span class="mord cjk_fallback">证</span></span></span><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-1.6599999999999993em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.000000000000001em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>A</mi><mo>+</mo><mi>B</mi><mo>⋅</mo><mi>C</mi><mo>=</mo><mo stretchy="false">(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo stretchy="false">)</mo><mo>⋅</mo><mo stretchy="false">(</mo><mi>A</mi><mo>+</mo><mi>C</mi><mo stretchy="false">)</mo><mover><mo stretchy="true">→</mo><mpadded width="+0.6em" lspace="0.3em"><mrow><mtext>当</mtext><mi>C</mi><mo>=</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover></mrow></mpadded></mover><mi>A</mi><mo>+</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mi>B</mi><mo>=</mo><mi>A</mi><mo>+</mo><mi>B</mi><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>4.5</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{gathered}        A + B \cdot C = (A + B) \cdot (A + C) \xrightarrow{当C = \overline{A}} A + \overline{A} \cdot B = A + B \qquad(式4.5) \\    \end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.9318310000000003em;vertical-align:-0.7159155000000001em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2159155000000001em;"><span style="top:-3.2159155000000004em;"><span class="pstrut" style="height:3.271831em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel x-arrow"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2718310000000002em;"><span style="top:-3.622em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight x-arrow-pad"><span class="mord mtight"><span class="mord cjk_fallback mtight">当</span><span class="mord mathdefault mtight" style="margin-right:0.07153em;">C</span><span class="mrel mtight">=</span><span class="mord overline mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9283300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight"><span class="mord mathdefault mtight">A</span></span></span><span style="top:-3.83033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line mtight" style="border-bottom-width:0.049em;"></span></span></span></span></span></span></span></span></span><span class="svg-align" style="top:-2.989em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="height:0.522em;min-width:1.469em;"><svg width="400em" height="0.522em" viewbox="0 0 400000 522" preserveaspectratio="xMaxYMin slice"><path d="M0 241v40h399891c-47.3 35.3-84 78-110 128-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.010999999999999899em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">4</span><span class="mord">.</span><span class="mord">5</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7159155000000001em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>证明</mtext><mo>:</mo><mtext>原式扩写为</mtext><mi>A</mi><mo>⋅</mo><mo stretchy="false">(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo>+</mo><mi>C</mi><mo stretchy="false">)</mo><mo>+</mo><mi>B</mi><mo>⋅</mo><mi>C</mi><mo stretchy="false">(</mo><mtext>说明</mtext><mo>:</mo><mtext>将</mtext><mo stretchy="false">(</mo><mi>B</mi><mo>+</mo><mi>C</mi><mo stretchy="false">)</mo><mtext>看成一个整体</mtext><mi>X</mi><mo separator="true">,</mo><mtext>以此类推</mtext><mo separator="true">,</mo><mtext>还可以将</mtext><mo stretchy="false">(</mo><mi>B</mi><mo>+</mo><mi>C</mi><mo>+</mo><mi>D</mi><mo>+</mo><mo>⋯</mo><mtext> </mtext><mo stretchy="false">)</mo><mtext>看成整体</mtext><mo stretchy="false">)</mo><mo separator="true">,</mo><mtext>故原式化为</mtext><mi>A</mi><mo>⋅</mo><mi>A</mi><mo>+</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>+</mo><mi>A</mi><mo>⋅</mo><mi>C</mi><mo>+</mo><mi>B</mi><mo>⋅</mo><mi>C</mi><mo>=</mo><mo stretchy="false">(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo stretchy="false">)</mo><mo>⋅</mo><mo stretchy="false">(</mo><mi>A</mi><mo>+</mo><mi>C</mi><mo stretchy="false">)</mo><mo separator="true">,</mo><mtext>得证</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{gathered}        证明:原式扩写为A \cdot (A + B + C) + B \cdot C(说明:将(B + C)看成一个整体X,以此类推,还可以将(B + C + D + \cdots)看成整体),故原式化为A \cdot A + A \cdot B + A \cdot C + B \cdot C = (A + B) \cdot (A + C),得证 \\\\\\    \end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.500000000000002em;vertical-align:-2.000000000000001em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.5000000000000004em;"><span style="top:-4.66em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord cjk_fallback">证</span><span class="mord cjk_fallback">明</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">原</span><span class="mord cjk_fallback">式</span><span class="mord cjk_fallback">扩</span><span class="mord cjk_fallback">写</span><span class="mord cjk_fallback">为</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mopen">(</span><span class="mord cjk_fallback">说</span><span class="mord cjk_fallback">明</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">将</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mclose">)</span><span class="mord cjk_fallback">看</span><span class="mord cjk_fallback">成</span><span class="mord cjk_fallback">一</span><span class="mord cjk_fallback">个</span><span class="mord cjk_fallback">整</span><span class="mord cjk_fallback">体</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">以</span><span class="mord cjk_fallback">此</span><span class="mord cjk_fallback">类</span><span class="mord cjk_fallback">推</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">还</span><span class="mord cjk_fallback">可</span><span class="mord cjk_fallback">以</span><span class="mord cjk_fallback">将</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mclose">)</span><span class="mord cjk_fallback">看</span><span class="mord cjk_fallback">成</span><span class="mord cjk_fallback">整</span><span class="mord cjk_fallback">体</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">故</span><span class="mord cjk_fallback">原</span><span class="mord cjk_fallback">式</span><span class="mord cjk_fallback">化</span><span class="mord cjk_fallback">为</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">得</span><span class="mord cjk_fallback">证</span></span></span><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-1.6599999999999993em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.000000000000001em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>+</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mi>C</mi><mo>+</mo><mi>B</mi><mo>⋅</mo><mi>C</mi><mo>=</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>+</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mi>C</mi><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>4.6</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{gathered}        A \cdot B + \overline{A} \cdot C + B \cdot C = A \cdot B + \overline{A} \cdot C \qquad(式4.6) \\    \end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.54333em;vertical-align:-0.5216650000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.021665em;"><span style="top:-3.138335em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">4</span><span class="mord">.</span><span class="mord">6</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5216650000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>证明</mtext><mo>:</mo><mtext>原式扩写为</mtext><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>+</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mi>C</mi><mo>+</mo><mi>B</mi><mo>⋅</mo><mi>C</mi><mo>⋅</mo><mo stretchy="false">(</mo><mi>A</mi><mo>+</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo stretchy="false">)</mo><mo>=</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>+</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mi>C</mi><mo>+</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>⋅</mo><mi>C</mi><mo>+</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mi>B</mi><mo>⋅</mo><mi>C</mi><mo>=</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>⋅</mo><mo stretchy="false">(</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>+</mo><mi>C</mi><mo stretchy="false">)</mo><mo>+</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mi>C</mi><mo>⋅</mo><mo stretchy="false">(</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mi>C</mi><mo>+</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>+</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mi>C</mi><mo separator="true">,</mo><mtext>得证</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{gathered}        证明:原式扩写为A \cdot B + \overline{A} \cdot C + B \cdot C \cdot (A + \overline{A})=A \cdot B + \overline{A} \cdot C + A \cdot B \cdot C + \overline{A} \cdot B \cdot C = A \cdot B \cdot (A \cdot B + C) + \overline{A} \cdot C \cdot (\overline{A} \cdot C + B) = A \cdot B + \overline{A} \cdot C,得证 \\\\\\    \end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.543329999999999em;vertical-align:-2.0216649999999996em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.521665em;"><span style="top:-4.638335em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord cjk_fallback">证</span><span class="mord cjk_fallback">明</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">原</span><span class="mord cjk_fallback">式</span><span class="mord cjk_fallback">扩</span><span class="mord cjk_fallback">写</span><span class="mord cjk_fallback">为</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">得</span><span class="mord cjk_fallback">证</span></span></span><span style="top:-3.138335em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-1.6383350000000005em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.0216649999999996em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>+</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mi>C</mi><mo>+</mo><mi>B</mi><mo>⋅</mo><mi>C</mi><mo>⋅</mo><mi>D</mi><mo>=</mo><mi>A</mi><mo>⋅</mo><mi>B</mi><mo>+</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>⋅</mo><mi>C</mi><mspace width="2em"><mo stretchy="false">(</mo><mtext>式</mtext><mn>4.7</mn><mo stretchy="false">)</mo></mspace></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{gathered}        A \cdot B + \overline{A} \cdot C + B \cdot C \cdot D = A \cdot B + \overline{A} \cdot C \qquad(式4.7)     \end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.54333em;vertical-align:-0.5216650000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.021665em;"><span style="top:-3.138335em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.80333em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:2em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">式</span><span class="mord">4</span><span class="mord">.</span><span class="mord">7</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5216650000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.24999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mtext>证明</mtext><mo>:</mo><mtext>与式</mtext><mn>4.6</mn><mtext>同理</mtext></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">    \begin{gathered}        证明:与式4.6同理    \end{gathered}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5000000000000002em;vertical-align:-0.5000000000000002em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1em;"><span style="top:-3.16em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord cjk_fallback">证</span><span class="mord cjk_fallback">明</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord cjk_fallback">与</span><span class="mord cjk_fallback">式</span><span class="mord">4</span><span class="mord">.</span><span class="mord">6</span><span class="mord cjk_fallback">同</span><span class="mord cjk_fallback">理</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5000000000000002em;"><span></span></span></span></span></span></span></span></span></span></span></span></p>]]></content>
    
    
    
    <tags>
      
      <tag>计算机组成原理</tag>
      
      <tag>数字电路</tag>
      
      <tag>CPU</tag>
      
      <tag>逻辑门电路</tag>
      
    </tags>
    
  </entry>
  
  
  
  <entry>
    <title>Windows下Hexo个人静态博客建立（GitHubPages）</title>
    <link href="/2019/12/29/Windows%E4%B8%8BHexo%E4%B8%AA%E4%BA%BA%E9%9D%99%E6%80%81%E5%8D%9A%E5%AE%A2%E5%BB%BA%E7%AB%8B%EF%BC%88GitHubPages%EF%BC%89/"/>
    <url>/2019/12/29/Windows%E4%B8%8BHexo%E4%B8%AA%E4%BA%BA%E9%9D%99%E6%80%81%E5%8D%9A%E5%AE%A2%E5%BB%BA%E7%AB%8B%EF%BC%88GitHubPages%EF%BC%89/</url>
    
    <content type="html"><![CDATA[<h1>Windows 下 Hexo 个人静态博客建立（GitHub Pages）</h1><h2 id="特别感谢b站up：codesheep">特别感谢B站up：<a href="https://space.bilibili.com/384068749">CodeSheep</a></h2><h3 id="注：转载请注明出处">注：<a href="https://nekolio.github.io/"><strong>转载请注明出处</strong></a></h3><h2 id="1-准备工作">1. 准备工作</h2><h3 id="1-1-node-js">1.1 <a href="https://nodejs.org">Node.js</a></h3><p><a href="https://nodejs.org">https://nodejs.org</a><br>下载对应版本，默认安装即可</p><h3 id="1-2-git">1.2 <a href="https://git-scm.com/downloads">Git</a></h3><p><a href="https://git-scm.com/downloads">https://git-scm.com/downloads</a><br>下载对应版本，默认安装即可<br><em>tips：这里主要用到 Git Bush 充当 Linux 下终端的作用以及 push 到 GitHub</em></p><h4 id="可能遇到的问题及解决方法">可能遇到的问题及解决方法</h4><h5 id="1-2-1-如果使用cmd管理员执行-git-命令时遇到-非内外部命令或可执行程序-的错误提示">1.2.1 如果使用cmd管理员执行 git 命令时遇到  <strong>“非内外部命令或可执行程序”</strong>   的错误提示</h5><blockquote><p><em><strong>找到git安装路径中bin的位置和git安装路径中git-core的位置，并将路径复制到系统变量的path中保存并退出，最好重启计算机。</strong></em></p></blockquote><h3 id="1-3-在任意路径下创建一个独立文件夹">1.3 在任意路径下创建一个独立文件夹</h3><h2 id="2-安装-hexo-并在本地部署">2. 安装 Hexo 并在本地部署</h2><h3 id="2-1-在此文件夹下右键选择-git-bush-here">2.1 在此文件夹下右键选择 Git Bush Here</h3><blockquote><dir align="center">  <p><img src="/2019/12/29/Windows%E4%B8%8BHexo%E4%B8%AA%E4%BA%BA%E9%9D%99%E6%80%81%E5%8D%9A%E5%AE%A2%E5%BB%BA%E7%AB%8B%EF%BC%88GitHubPages%EF%BC%89/GitBush.png" alt="Git Bush Here"></p></dir>  </blockquote><h4 id="或者打开-git-bush-cd-到该文件夹下">或者打开 Git Bush ，cd 到该文件夹下</h4><blockquote><dir align="center">  <p><img src="/2019/12/29/Windows%E4%B8%8BHexo%E4%B8%AA%E4%BA%BA%E9%9D%99%E6%80%81%E5%8D%9A%E5%AE%A2%E5%BB%BA%E7%AB%8B%EF%BC%88GitHubPages%EF%BC%89/cd.png" alt="Git Bush cd"></p></dir>  </blockquote><h3 id="2-2-检查-node-和-npm-的安装">2.2 检查 node 和 npm 的安装</h3><p>分别输入<code>node -v</code>，<code>npm -v</code></p><blockquote><dir align="center">  <p><img src="/2019/12/29/Windows%E4%B8%8BHexo%E4%B8%AA%E4%BA%BA%E9%9D%99%E6%80%81%E5%8D%9A%E5%AE%A2%E5%BB%BA%E7%AB%8B%EF%BC%88GitHubPages%EF%BC%89/check.png" alt="Git Bush check"></p></dir>  </blockquote><h3 id="2-3-安装-hexo-并在本地部署">2.3 安装 Hexo 并在本地部署</h3><p><strong>tips:此处安装 cnpm 以改善 Hexo 镜像下载速度（taobao源）</strong></p><ol><li><p>安装 <code>npm install -g cnpm --registry=https://registry.npm.taobao.org</code> ，等待安装完成</p></li><li><p>测试 <code>cnpm</code>，无错误提示即安装成功</p></li><li><p>安装 Hexo <code>cnpm install -g hexo-cli</code>，等待安装完成</p></li><li><p>测试 <code>hexo -v</code>，无错误提示即安装成功</p></li><li><p>检查 终端/cmd 当先工作路径是否在原自建文件夹下<br>Git Bush输入：<code>pwd</code><br>cmd输入：<code>chdir</code></p></li><li><p>初始化hexo <code>hexo init</code> （这一步前提要安装Git），等待安装完成</p></li></ol><p><strong>到此 Hexo 已基本在本地部署</strong><br>7. 本地测试，输入 <code>hexo -s</code> (hexo -start)，得到端口，在浏览器输入端口地址查看效果，在终端 Ctrl + c 可以停止测试</p><h2 id="3-将-hexo-push-到远端部署-github">3. 将 Hexo push 到远端部署（<a href="https://www.github.com">GitHub</a>）</h2><h3 id="3-1-在-github-上新建-repository">3.1 在 GitHub 上新建 repository</h3><blockquote><p><img src="/2019/12/29/Windows%E4%B8%8BHexo%E4%B8%AA%E4%BA%BA%E9%9D%99%E6%80%81%E5%8D%9A%E5%AE%A2%E5%BB%BA%E7%AB%8B%EF%BC%88GitHubPages%EF%BC%89/GitHub.png" alt="GitHub"></p></blockquote><p><strong>注意：要记得打开 Pages</strong></p><blockquote><p><img src="/2019/12/29/Windows%E4%B8%8BHexo%E4%B8%AA%E4%BA%BA%E9%9D%99%E6%80%81%E5%8D%9A%E5%AE%A2%E5%BB%BA%E7%AB%8B%EF%BC%88GitHubPages%EF%BC%89/pages.png" alt="GitHub Pages"></p></blockquote><h3 id="3-2-配置-config-yml">3.2 配置 <code>_config.yml</code></h3><ol><li><p>在自建文件夹下找到 <code>_config.yml</code> ，以文本形式打开</p></li><li><p><strong>找到</strong></p></li></ol><pre><code class="language-html">deploy:type: ''  </code></pre><p><strong>修改为</strong></p><pre><code class="language-html">deploy:type: 'git'repo: 仓库地址branch: master  </code></pre><p><strong>其中，仓库地址为所建仓库地址，例如 <code>https://github.com/nekolio/nekolio.github.io.git</code></strong><br><strong>另外，注意冒号后的空格以及 type 的单引号</strong></p><h3 id="3-3-安装-git-部署插件-完成远端部署">3.3 安装 Git 部署插件，完成远端部署</h3><ol><li><p>回到 终端/cmd ，输入 <code>cnpm install --save hexo-deployer-git</code> 安装 Git 部署工具（这一步前提要安装Git），等待安装完成。</p></li><li><p>三部曲<br><code>hexo clean</code> 清除缓存文件 (db.json) 和已生成的静态文件 (public)。<br><code>hexo g</code> (hexo generate) 生成静态文件。<br><code>hexo d</code> (hexo deploy) 部署网站。<br>以上均无错误提示即成功。</p></li></ol><p><strong>到此 Hexo 的远端部署已基本完成</strong><br><strong>访问 Pages 即可，例如 <a href="https://nekolio.github.io">https://nekolio.github.io</a></strong></p><h2 id="4-补充">4. 补充</h2><h3 id="4-1-hexo-主题设置">4.1 Hexo 主题设置</h3><ol><li>download/clone Hexo 的主题到 themes 文件夹下，例如<br><code>git clone https://github.com/litten/hexo-theme-yilia.git themes/yilia</code> 等待完成。</li><li>配置 <code>_congig.yml</code> ：</li></ol><p>找到<br><code>theme: landscape</code><br>改成 <code>theme: yilia</code> 即可</p><ol start="3"><li>完成三部曲推送到远端</li></ol><h3 id="4-2-hexo-markdown-里添加图片无法显示问题">4.2 Hexo Markdown 里添加图片无法显示问题</h3><ol><li>配置 <code>_congig.yml</code> ：</li></ol><p>找到 <code>post_asset_folder: false</code><br>改成 <code>post_asset_folder: true</code><br><strong>此时 <code>hexo n</code> 命令新建md文件时会自动生成一个同名文件夹，将图片放在此文件夹下后即可在md中引用</strong></p><ol start="2"><li>终端输入 <code>npm install hexo-asset-image --save</code><br>或<br><code>npm install https://github.com/CodeFalling/hexo-asset-image --save</code><br>安装此图片插件</li><li>完成三部曲推送到远端</li></ol><h2 id="5-参考资料">5.参考资料</h2><ol><li>视频：<a href="https://www.bilibili.com/video/av44544186">手把手教你从0开始搭建自己的个人博客, UP:CodeSheep</a></li><li>文档：<a href="https://hexo.io/zh-cn/docs/">Hexo 文档</a></li><li>另附：<a href="https://www.codesheep.cn">CodeSheep博客</a></li></ol>]]></content>
    
    
    
    <tags>
      
      <tag>Windows</tag>
      
      <tag>Hexo</tag>
      
      <tag>GitHub</tag>
      
      <tag>Git</tag>
      
      <tag>node.js</tag>
      
      <tag>npm</tag>
      
      <tag>CodeSheep</tag>
      
      <tag>Blog</tag>
      
      <tag>博客</tag>
      
    </tags>
    
  </entry>
  
  
  
  <entry>
    <title>Markdown基础语法</title>
    <link href="/2019/12/29/Markdown%E5%9F%BA%E7%A1%80%E8%AF%AD%E6%B3%95/"/>
    <url>/2019/12/29/Markdown%E5%9F%BA%E7%A1%80%E8%AF%AD%E6%B3%95/</url>
    
    <content type="html"><![CDATA[<h1>Markdown基础语法</h1><hr><h2 id="字体样式">字体样式</h2><h3 id="1-一级标题">1. 一级标题</h3><pre><code>Markup1:# 一级标题 #or Markup2:一级标题==</code></pre><p>注意：<br><em>1.Markup1中右 “#” 可以省略，同时注意左 “#” 后要至少输入一个空格之后再输入标题</em></p><p><strong>效果如下：</strong></p><blockquote><div align="center">  <h1>一级标题</h1></div></blockquote><h3 id="2-二级及多级标题">2. 二级及多级标题</h3><pre><code>Markup1:## 二级标题 ##or Markup2:二级标题--</code></pre><p>注意：<br><em>1.Markup1中，右 “#” 可以省略，同时注意左 “#” 后要至少输入一个空格之后再输入标题</em><br><em>2.以此类推，</em><code>### 三级标题 ###</code>，<code>#### 四级标题 ####</code>，<code>##### 五级标题 #####</code>，<code>###### 六级标题 ######</code>，<em>最多到六级标题。</em></p><p><strong>效果如下：</strong></p><blockquote><div align="center">  <h2 id="二级标题">二级标题</h2><h3 id="三级标题">三级标题</h3><h4 id="四级标题">四级标题</h4><h5 id="五级标题">五级标题</h5><h6 id="六级标题">六级标题</h6></div></blockquote><h3 id="3-斜体">3. 斜体</h3><pre><code>Markup1:*斜体*or Markup2:_斜体_</code></pre><p>注意：<br><em>1.星号或下划线中间不用输入空格隔开</em></p><p><strong>效果如下：</strong></p><blockquote><div align="center">  <p><em>斜体</em></p></div>  </blockquote><h3 id="4-粗体">4. 粗体</h3><pre><code>Markup1:**粗体**or Markup2:__粗体__</code></pre><p>注意：<br><em>1.星号或下划线中间不用输入空格隔开</em></p><p><strong>效果如下：</strong></p><blockquote><div align="center">  <p><strong>粗体</strong></p></div></blockquote><h3 id="5-粗斜体">5. 粗斜体</h3><pre><code>Markup1:***粗斜体***or Markup2:___粗斜体___</code></pre><p>注意：<br><em>1.星号或下划线中间不用输入空格隔开</em></p><p><strong>效果如下：</strong></p><blockquote><div align="center">  <p><em><strong>粗斜体</strong></em></p></div></blockquote><h3 id="6-删除线">6. 删除线</h3><pre><code>Markup:~~删除线~~</code></pre><p><strong>效果如下：</strong></p><blockquote><div align="center">  <p><s>删除线</s></p></div></blockquote><h3 id="7-正文书写">7. 正文书写</h3><p><code>Markup:直接输入正文内容</code></p><h3 id="8-缩进">8. 缩进</h3><pre><code>Markup:&amp;nbsp;缩进1/4个&amp;ensp;缩进半个   &amp;emsp;缩进一个</code></pre><p><strong>效果如下：</strong></p><blockquote><p> 缩进1/4个中文字符的长度<br>第二行<br> 缩进半个中文字符的长度<br>第二行<br> 缩进一个中文字符的长度<br>第二行</p></blockquote><hr><h2 id="列表">列表</h2><h3 id="1-无序列表及其多级列表">1. 无序列表及其多级列表</h3><pre><code>Markup1:+ 无序列表第一级  + 无序列表第二级    + 无序列表第三级      + 无序列表第四级or Markup2:- 无序列表第一级  - 无序列表第二级    - 无序列表第三级      - 无序列表第四级or Markup3:* 无序列表第一级  * 无序列表第二级    * 无序列表第三级      * 无序列表第四级</code></pre><p>注意：<br><em>1.星号或加号或减号中间要输入空格隔开，这点容易与字体样式混淆</em></p><p><strong>效果如下：</strong></p><blockquote><ul><li>无序列表第一级</li><li>无序列表第二级<ul><li>无序列表第三级<ul><li>无序列表第四级</li></ul></li></ul></li></ul></blockquote><h3 id="2-有序列表">2. 有序列表</h3><pre><code>Markup:1. 有序列表第一项  2. 有序列表第二项  3. 有序列表第三项</code></pre><p>注意：<br><em>1.数字 + . + 空格 +内容</em></p><p><strong>效果如下：</strong></p><blockquote><ol><li>有序列表第一项</li><li>有序列表第二项</li><li>有序列表第三项</li></ol></blockquote><hr><h2 id="引用与脚注">引用与脚注</h2><h3 id="1-引用与多级引用">1. 引用与多级引用</h3><pre><code>Markup:&gt;引用&gt;&gt;二级引用&gt;&gt;&gt;多级引用</code></pre><p><strong>效果如下：</strong></p><blockquote><p>引用</p><blockquote><p>二级引用</p><blockquote><p>多级引用</p></blockquote></blockquote></blockquote><h3 id="2-脚注">2. 脚注</h3><pre><code>Markup:内容1[^1]  内容2[^2][^1]: 第一个脚注[^2]: 第二个脚注</code></pre><p>注意：<br><em>1.脚注功能兼容性比较差，目前少用</em><br><em>2.[^]里的内容（ID）随意但不能重复</em><br><em>3.内容与脚注要注意隔行，脚注内容可以在文档任意位置。</em></p><p><strong>效果如下：</strong></p><blockquote><p>内容1<a href="%E7%AC%AC%E4%B8%80%E4%B8%AA%E8%84%9A%E6%B3%A8">^1</a><br>内容2<a href="%E7%AC%AC%E4%BA%8C%E4%B8%AA%E8%84%9A%E6%B3%A8">^2</a></p></blockquote><hr><h2 id="链接与图片插入">链接与图片插入</h2><h3 id="1-链接">1. 链接</h3><pre><code>行内式Markup:[我的博客](https://nekolio.github.io &quot;nekolio的博客&quot;)</code></pre><pre><code>参考式Markup:[我的博客][url1][url1]: https://nekolio.github.io &quot;nekolio的博客&quot;</code></pre><pre><code>显示式Markup:&lt;https://nekolio.github.io&gt;</code></pre><p>注意：<br><em>1.标识与标识声明要注意隔行，声明链接可以在文档任意位置。</em></p><p><strong>效果如下：</strong></p><blockquote><p>行内式：<br><a href="https://nekolio.github.io" title="nekolio的博客">nekolio的博客</a></p><p>参考式：<br><a href="https://nekolio.github.io" title="nekolio的博客">nekolio’s blog</a></p><p>显示式：<br><a href="https://nekolio.github.io">https://nekolio.github.io</a></p></blockquote><h3 id="2-图片">2. 图片</h3><pre><code>Markup:![图像名称](相对路径/绝对路径)![MuseDash](Markdown基础语法/MuseDash.png &quot;Muse Dash&quot;)</code></pre><p>注意：<br><em>1.链接的参考式在图片中可套用</em></p><p><strong>效果如下：</strong></p><blockquote><p><img src="/2019/12/29/Markdown%E5%9F%BA%E7%A1%80%E8%AF%AD%E6%B3%95/MuseDash.png" alt="MuseDash" title="Muse Dash"></p></blockquote><hr><h2 id="代码行与代码块">代码行与代码块</h2><h3 id="1-代码行">1. 代码行</h3><pre><code>Markup:`printf(&quot;Hello World!&quot;);`</code></pre><p><strong>效果如下：</strong></p><blockquote><p><code>printf(&quot;Hello World!&quot;);</code></p></blockquote><h3 id="2-代码块">2. 代码块</h3><pre><code>Markup:  \`\`\`java  System.out.println(&quot;Hello World!&quot;);  System.out.println(&quot;nekolio&quot;);  \`\`\`  </code></pre><p>注意：<br><em>1.“java”处可以替换成该代码块所用语言，</em> \ <em>是转义符，要去掉</em></p><p><strong>效果如下：</strong></p><blockquote><pre><code class="language-java">System.out.println(&quot;Hello World!&quot;);System.out.println(&quot;nekolio&quot;);</code></pre></blockquote><hr><h2 id="分割线">分割线</h2><pre><code>Markup1:  ___  Markup2:***</code></pre><p><strong>效果如下：</strong></p><blockquote><hr></blockquote><hr><h2 id="表格">表格</h2><pre><code>Markup:|        | 第一列 | 第二列 | 第三列 || :----: | :----- | :----: | -----: || 第一行 | 居左1  | 居中2  |  居右3 || 第二行 | 居左4  | 居中5  |  居右6 || 第三行 | 居左7  | 居中8  |  居右9 |</code></pre><p>注意：<br><em>1.</em> | <em>符号不能漏（最后一列可省）</em><br><em>2.居左 <code>:-</code>，居中 <code>:-:</code>，居右 <code>-:</code></em></p><p><strong>效果如下：</strong></p><blockquote><table><thead><tr><th style="text-align:center"></th><th style="text-align:left">第一列</th><th style="text-align:center">第二列</th><th style="text-align:right">第三列</th></tr></thead><tbody><tr><td style="text-align:center">第一行</td><td style="text-align:left">居左1</td><td style="text-align:center">居中2</td><td style="text-align:right">居右3</td></tr><tr><td style="text-align:center">第二行</td><td style="text-align:left">居左4</td><td style="text-align:center">居中5</td><td style="text-align:right">居右6</td></tr><tr><td style="text-align:center">第三行</td><td style="text-align:left">居左7</td><td style="text-align:center">居中8</td><td style="text-align:right">居右9</td></tr></tbody></table></blockquote><hr><h2 id="未完待续">未完待续</h2><p><a href="#Markdown%E5%9F%BA%E7%A1%80%E8%AF%AD%E6%B3%95" title="Goto 标题">返回顶部</a></p>]]></content>
    
    
    
    <tags>
      
      <tag>Markdown</tag>
      
      <tag>语法</tag>
      
    </tags>
    
  </entry>
  
  
  
  
</search>