# Complement Arithmetic - Computer Logical Organization

## What are complements?

The magical manipulations and the subtraction operation is simplified by complements. Complements are of two types for each of the radix system, which are as follows:

 S.N. Complement Description 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

## What are the Binary system complements?

The two different types of complements for the binary system are 2’s complement and 1’s complement as the binary system has base 2 and hence r=2.

### 1's complement

By changing all 1’s to 0’s and vice versa, the 1’s complement of the number is identified. The following is the example of 1’s complement:

### 2's complement

For the LSB of the 1’s complement of the number, when 1 is added it results in 2’s complement of the binary number.

2's complement = 1's complement + 1

The following is the example of 2's Complement: