When using two's complement, the most significant bit (the furthest left) is negative.

i.e. In Normal (Unsigned) binary:

 128  64  32  16  8  4  2  1

In two's complement the columns are:

-128  64  32  16  8  4  2  1

Method:

1. Represent positive value in binary         00110101 (53)

2. Flip all of the bits (swap 1s and 0s)       11001010

3. Add 1 to the result                              11001011 (-53)

Binary subtraction of numbers can be done by adding the 2's complement of the second number to the first number. Binary subtraction is just the binary addition of a negative number.

Example Question:

Calculate the result of 63 - 24 using binary

The first step would be to convert 24 into two’s complement to create -24:

0001 1000 → 1110 0111 → 1110 1000 = -24

After this, we can then add the binary equivalent of 63 to what we just found for -24.

Add the 63 to -24

   0 0 1 1 1 1 1 1

+ 1 1 1 0 1 0 0 0

1 0 0 1 0 0 1 1 1

This leaves with a final answer of:

0010 0111 = 39

Note how the 1 that carried over to the end on the left has disappeared. This is because the final answer was positive, and we were only using 8 bits. You can ignore that 1 as it is an overflow.