Arithmetic Complements in Computer Architecture

Arithmetic Complements – Complements are used in digital computers in order to simplify the subtraction operation and for logical manipulations. For each radix-r system (radix r represents the base of the number system), there are two types of complements.

1. Radix Complement: The radix complement is referred to as the r’s complement.
2. Diminished Radix Complement: The diminished radix complement is referred to as the (r-1)’s complement.

Binary System Complements

As the binary system has base r=2. So the two types of complements for the binary system are 2’s complement and 1’s complement.

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 taking the complement or 1’s complement.

An example of 1’s complement is as follows.

Given number = 10101
1's complement = 01010

Let’s take an example to find out the 1’s complement of a given number

Given number = 10011
1's complement = 01100

2’s complement: The 2’s complement of a binary number is obtained by adding 1 to the Least Significant Bit (LSB) of the 1’s complement of the number. 2’s complement = 1’s complement + 1.

An example of 2’s complement is as follows.

Given number   = 10101
1's complement = 01010
Add +                1
               = 01011

Let’s take an example to find out the 2’s complement as follows.

Given number   = 11010010
1's complement = 00101101
Add +                   1
               = 00101110