Negation
In sign-magnitude representation, the rule for forming the negation of an integer is simple: Invert the sign bit.

In twos complement representation, the negation of an integer can he formed with the following rules:

1. Take the Boolean complement of each bit of the integer (including the sign bit). That is. set each 1 to 0 and each 0 to 1.

2. Treating the result as an unsigned binary integer, add 1.

This two-step process is referred to as the twos complement operation, or the taking of the twos complement of an integer

Example:

Figure 2

Negation Special Case 1:

0 = 00000000

Bitwise not 11111111

Add 1 to LSB +1

Result 1 00000000

Overflow is ignored, so: - 0 = 0

Negation Special Case 2:

-128 = 10000000

bitwise not 01111111

Add 1 to LSB +1

Result 10000000

So: -(-128) = -128.

Because 128 is out of the range of signed 8bits numbers.

Addition and Subtraction:
Addition and Subtraction is done using following steps:

Normal binary addition
Monitor sign bit for overflow
Take twos compliment of subtrahend and add to minuend ,i.e. a - b = a + (-b)