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.

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