Ok so this is more so I don’t forget it, than because I think anyone will read it or care. But on the off chance you care about this kind of thing, here is what I learned about binary:

The position of the number indicates a multipul of the base of the number system (2) the same as what we have in the human base 10 number system.

So a 1 in the ones column gives us 1: 0001

And a one in the twos column would give us two: 0010

A one in both the ones and twos column gives us three: 0011

And the columns double in value as they move left. So 0100 is four, and 1000 is eight and adding a fifth column will give us sixteen and so on.

Adding:

Adding binary numbers is pretty simple.

0+0=0

0+1=1

1+1 = 0 and carry 1 to the next column.

1+1+ a carry of one = 1 and a carry of one.

So:

0111 (aka 7)

+0111

——–

1110 (aka 14)

Subtraction:

Ok this is a little weird. Computers don’t subtract. Well they do, but they do it by adding a negative to a positive. To create the negative number, called a twos compliment, you need to flip all the bits (change all the ones to zeros and vice versa) and then add one. It sounds simple but I screw it up pretty consistently, so I was very happy to find an idiot resistant method of finding a twos compliment just in time for my final exam:

Working from right to left, ignore any zeros and find the first one. Keep it the way it is flip all the other bits like so:

0111 (aka 7)

1001 (the twos compliment of 7)

so:

1110 (aka 14)

+1001 (plus the twos compliment of 7)

——-

0111 (equals 7!)

Technically it equals 10111 but computers can only work with so many bits at a time (the newest can now do 64 bits at a time, older ones just 32). In this case we are working with 4 bit numbers so any carrys from the addition will just be dropped. So the 1 on the far left will be chopped off leaving us with the 0111.

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