1’s Complement and 2’s Complement

Complement Systems

The 1’s complement and 2’s complement systems are methods used to represent negative numbers in binary and simplify arithmetic operations in digital electronics.
1’s Complement: 

Definition

1’s complement of a binary number is obtained by flipping all bits in the number:

• Change all 0s to 1s.
• Change all 1s to 0s.
  – Invert all bits (0 to 1 and 1 to 0).

Example

• Binary number: 10101.
• 1’s complement: 01010.

2’s Complement:

Definition

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

2’s complement=(1’s complement)+1.
– Add 1 to the 1’s complement.
– Used for representing negative numbers in binary.