# 1s Complement `number` Discussion.

On this page we are going to discuss 1s complement in details with binary logic examples. Binary numbers can also be represented by ‘radix’ and ‘radix -1’ forms.

In binary arithmetic, 1s complement of a binary number N is obtained by the formula below:

`(2^n – 1) – N`, Where n is the no of bits in binary number N.

Example: Convert binary number 111001101 to 1’s complement.

Method: By following the equation `above`, we have N = 111001101, n = 9

Now 2^n = 256. In binary, 100000000

2^n -1 = 255. In binary, 11111111 --> Represent this as TERM I

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Now represent 1s complement as subtraction of TERM I (=011111111), note extended by extra 0 for subtraction. TERM II as N (=111001101).

1’s complement of N = TERM I(or 100000000 – 1) -111001101

So we have subtraction below as I - II.

011111111

– 111001101

= 000110010

Answer: 1’s complement of N is 000110010

`Alternate approach` to get ones complement :

Invert all the bits of the binary number

N = 111001101

1’s complement of N is 000110010

Refer 2’ s Complement from here.

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