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:

Radix Complement
The radix complement is referred to as the r's complement
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:

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:

2's Complement

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