Binary Arithematic Operations

1’s Complement : 1’s complement of binary is obtained by subtracting each bit by 1 . We can get 1’s complement by simply replacing 1 by 0 and 0 by 1. 1’s Complement of 1011 is 0100.

2’s Complement:2’s Complement of binary number is obtained by adding binary 1 to the 1’s complement of the number.

Example of 2’s complement of 1101101 = ?

                     1’s complement = 0010010

                                                                     +1

                      2’s complement = 10011

Subtraction of binary number using 1’s complement:

Steps:-

i.                     Make both the numbers of having the same bit.

ii.                   Determine the 1’s complement of the number to be subtracted.

iii.                  Add the first complement to the given number from which we subtract.

iv.                 If there exist any additional bits(carry) in the result after addition, remove and add to the result else Determine the 1’s complement of the result and prefix by negative sign to get the final result.

For example : Subtract 1110000 from 1100000 1’s complement of 110000 = 0001111 . Adding it with minuend = 0001111+1100000 = 1101111

Since, there exist no any additional bit 1’s complement of 1101111 is 0010000.

Hence, Difference will be – 0010000.

Subtraction using 2’s complement.

a)      Make both the number having same number of bit.

b)      Determine the 2’s complement of the number to be subtracted.

c)       Add the 2’s complement to the given number from which we subtract(minuend).

d)      If there exist any additional bit(carry) in the result after addition neglect the carry and the remaining bits is the required answer else,Determine the 2’s complement of the result and prefix by negative sign to get the final result.

For example : 111000-110000

2’s complement of 111000 = 0001111+1=0010000

Adding it with minuend = 0010000+1100000 = 1110000

2’s Complement of 1110000=0001111+1 = -001000