## 1's complement vs 2's complement-Difference between 1's complement and 2's complement

This page on 1's complement vs 2's complement describes basic difference between 1's complement and 2's complement.

### 1's complement

The formula for finding **1's complement** of a number is as follows:

N' = (2^{n} - 1) - N

Where,

n = number of bits per word

N = Positive Integer

N' = -N in 1's complement Notation

EXAMPLE:

Input: 8 bit word, N = 6

N' = (2^{8} - 1) - 6

N' = 249

N' = (11111001)_{2}

How to find 1's complement of a binary number:

In order to find 1's complement take bit by bit complement of the binary number.

EXAMPLE: N = 6 = (00000110)_{2}

1's complement of N = N' = (11111001)_{2}

### 2's complement

The formula for finding **2's complement** of a number is as follows:

N^{*} = 2^{n} - N

Where,

n = number of bits per word

N = Positive Integer

N^{*} = -N in 2's complement Notation

EXAMPLE:

Input: 8 bit word, N = 6

N^{*} = 2^{8} - 6

N^{*} = 250

N^{*} = (11111010)_{2}

How to find 2's complement of a binary number:

In order to find 2's complement; start at the right end of the binary number and
complement each bit to the left of the first "1" in the number.

EXAMPLE: N = 6 = (00000110)_{2}

2's complement of N = N^{*} = (11111010)_{2}

### Find 2's complement from 1's complement

➨In order to determine 2's complement, add 1 to LSB of 1's complement.

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