Two’s Complement is a mathematical operation on Binary Numbers. This operation has many real-life applications like the implementation of subtractions and the storage of negative integers.

In this article, we will do an in-depth analysis of Two’s Complement, which includes its calculation, applications, and implementation in C++.

Before we understand the concept of Two’s Complement, we need to study One’s Complement.

Understanding One’s Complement

This operation reverses each bit in the binary number. For instance, considering a binary number = 1001001

One’s complement of a binary number

As seen in the above figure, One’s Complement is the reversal of each bit of a binary number.

Understanding Two’s Complement

In addition to applying One’s Complement, Two’s Complement include adding 1 to the One’s Complement. Carrying forward the previous example, we see:

Example of Two’s Complement

As a result, Two’s complement involves “reversing the bits” and “adding 1 to the reversed bits”. This operation may seem trivial at first, but it forms the underlying concept of all subtractions in modern systems.

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