# Perform the 8-bit two's complement binary sum 17 - 24

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The first step is to view the sum as an addition of a positive and a negative number, rather than a subtraction:

17 + (-24)

From there we can work out the binary equivalents of the 2 numbers:

b7   b6   b6   b4   b3   b2   b1   b0

17      0     0     0     1     0     0     0     1

24      0     0     0     1     1     0     0     0

24 then has to be converted into it's equivalent negative number in two's complement. This is done in 2 steps:

1. Flip all the bits in the number

2. Peform binary addition of new number and 1.

So first we flip all the bits:

b7   b6   b6   b4   b3   b2   b1   b0

1     1     1     0     0     1     1     1

b7   b6   b6   b4   b3   b2   b1   b0

1     1     1     0     0     1     1     1

0     0     0     0     0     0     0     1

1     1     1     0     1     0     0     0

This gives us the two's complement representation of -24.

Then we simply perform the additon of 17 and -24 in binary:

b7   b6   b6   b4   b3   b2   b1   b0

0     0     0     1     0     0     0     1

1     1     1     0     1     0     0     0

1     1     1     1     1     0     0     1

Which, as expected, is the binary representation of -7 (you can check this by performing the same 2 stage method to convert the number back to positive 7, then back into decimal from there).

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