1.3.3 BINARY COMPLEMENTS

Complements are used in the digital computers in order to simplify the subtraction operation and for the logical manipulations.

1's complement

The 1's complement of a number is found by changing all 1's to 0's and all 0's to 1's. This is called as taking complement or 1's complement.

Example of 1's Complement is as follows:

 1011001         à        0100110

 10000             à        01111

 11011             à        00100

2's complement

The 2's complement of binary number is obtained by adding 1 to the Least Significant Bit (LSB) of 1's complement of the number.

2's complement = 1's complement + 1

Example of 2's Complement is as follows:

  0101              à        1010 + 1          =          1011

  101100          à        010011 + 1      =          010100

  0000              à        1111 + 1          =          10000

  111                à        000 + 1            =          001