The 1’s complement and the 2’s complement of a binary number are important because

they permit the representation of negative numbers. The method of 2’s complement arithmetic is commonly used in computers to handle negative numbers

Finding the 1’s Complement

The 1’s complement of a binary number is found by changing all 1s to 0s and all 0s to 1s,
as illustrated below:


Finding the 2’s Complement

The 2’s complement of a binary number is found by adding 1 to the LSB of the 1’s complement.

2's complement = (1's complement) + 1

 Example 1

Find the 2’s complement of 10110010.

Solution:


An alternative method of finding the 2’s complement of a binary number is as follows:

  1. Start at the right with the LSB and write the bits as they are up to and including the first 1.
  2. Take the 1’s complements of the remaining bits.

 Example 2 

Find the 2’s complement of 10111000 using the alternative method.

Solution