Representing Negative Integers 

All numbers belong to the set or group called real numbers 

Inside the set of real numbers is a set of all positive and negative whole numbers.  A better way of representing negative numbers is by using Two’s Complement. 

Two’s  Complement is deigned so that the set of integers show symmetry about zero.

To find the Two’s Complement  of a number :

• Change all the 1’s to 0 and 0’s to 1
• Add 1

Example 1

How would – 5 be represented using two complement?

5 = 0 0 0 0 0 1 0 1

Change all the 1’s to 0 and 0’s to 1

0 0 0 0 0  1 0 1
1 1 1 1 1 0 1 0

Add 1 

1 1 1 1 1 0 1 0
0 0 0 0 0 0 0 1 +
1 1 1 1 1 0 1 1

So -5 as Two Complement = 1 1 1 1 1 0 1 1 

Example 2

How would – 88 be represented using two complement?

88 = 0 1 0 1 1 0 0 0

Change all the 1’s to 0 and 0’s to 1

0 1 0 1 1 0 0 0
1 0 1 0 0 1 1 1

Add 1 

1 0 1 0 0 1 1 1
0 0 0 0 0 0 0 1 +
1 0 1 0 1 0 0 0

So -88 as Two Complement = 1 0 1 0 1 0 0 0