# Difference between 1’s complement and 2’s complement – Binary Number system

**Table of content**

## One’s Complement

The 1’s complement of a binary number is obtained by complementing all its bits, i.e. by replacing 0s with 1’s and 1’s with 0s.

**Example:** Find the one’s complement of (10010110)_{2 }

Solution:

Replace 1’s by 0’s and 0’s by 1’s

The 1’s complement of (10010110)_{2} is (01101001)_{2}.

## Two’s Complement

The 2’scomplement of a binary number is obtained by adding 1’ to its 1’s complement.

**Example:** Find the one’s complement of (10010110)_{2 }

Solution: Find the one’s complement by replacing 1’s by 0’s and 0’s by 1’s

(01101001)_{2}.

To determine the 2’s complement add 1 to the one’s complement

The 2’s complement of (10010110)_{2 }is (01101010)_{2}.