lesson10.txt

#color 0xffc3e1fe
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#title The Subframe Lessons
#title 110: Binary Numbers

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#section 10.1 Binary Numbers

Many computations involve numbers.
However, logic gates only understand ON/OFF states.

In computer jargon, ON/OFF states are called "bits".

Binary is a way to represent numbers using bits.

To represent a number in binary, we break it up into powers of two,
always preferring larger powers:

#space 12

5 = 4 + 1      11 = 8 + 2 + 1      187 = 128 + 32 + 16 + 8 + 2 + 1

Note that we will never have more than one of each power.
If we have two 4s, for example, we would prefer to use an 8 instead.

We assign each bit to a power of two.
We turn the bit ON if the power of two is present, and OFF if it isn't.

Here's a binary converter that you could use to get a better feel
for binary.

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#section Activity #10.1

Convert the following numbers
to binary by hand:

3, 10, 35, 88

Parse the following binary
numbers by hand:

10, 111, 1100, 10100

Use the decimal-to-binary
converter to check your answers.

#section Activity #10.2

Make a circuit that multiplies an
8-bit binary number by 8.

#answer 150 30

#section Activity #10.3

Make a circuit that outputs ON if
two 4-bit numbers are the same.

This doesn't need to be subframe.

#answer 160 50