Compliment representation of numbers

In sign magnitude system the sign of a binary number is denoted by a extra bit in-front of the number.

For example +5 is denoted by 0,101.

0 : show that the number is positive

1: show that the number is negative

Ones compliment

In ones compliment system the representation of positive number is the same as that of sign magnitude system. But the representation of negative number is different.

For example -5 is represented in ones compliment as 1,010. This is obtained by replacing all the 1s by 0 and zero by 1 in the binary representation of +5 which is 0,101.

The process of replacing a 0 by 1 and 1 by 0 is called bits complimenting.

In general a n bit number x's (with out sign bit) ones compliment is given by (2^n-1-x).

Twos compliment

The twos compliment is obtained by adding 1 to the ones compliment of a number.

Example:

+5=0,101

-5=1,010 (1s compliment)

now twos compliment of -5 is 1,010 + 0001 = 1,011

In general for an n bit number twos compliment is given by 1,(2^n-x). Another method to to find the twos compliment of a binary number is to scan the number from left to right and compliment all the bits appearing after the first one. An example I given below.

0,1110 → 1,0010