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## 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' = (2n - 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' = (28 - 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* = 2n - 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* = 28 - 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.