Complements

Complements are used in digital circuits, as they simplify the subtraction operation. It is faster to subtract by adding complements than by performing true subtraction.

One’s Complement

When in a binary number, each bit is inverted i.e. 1 is inverted into 0 and 0 is inverted into 1. The number we get as a final result is 1’s complement of the given binary number.

Suppose the given binary number is 01011000101 and we have to find its 1’s complement.

1's complement for 01011000101 is 10100111010.

Two’s Complement

The two’s complement is a method for representing signed binary numbers. It is also used for performing arithmetic operations. To form the two’s complement, we just add 1 to the one’s complement.

 Suppose the given binary number is 1100101. So the first step is to find its 1’s complement.

Now as we have got the 1’s complement, we will add 1 in it to get 2’s complement.

So 2’s complement of 1100101 is 0011011.

9's and 10's Complement

We use 1's complement and 2's complement when we have a binary number. But if in case, when we have a decimal number, we use the 9's and 10's complement. The 10's complement is obtained from the 9's complement of the number as 2’s complement is obtained from 1’s complement.

9's Complement

The 9's complement is used in subtraction of the decimal numbers. The 9's complement of a number is calculated by subtracting each digit of the number by 9.

Let us see an example. We have to find the 9’s complement of the given decimal number 2143. For this, we subtract each digit of the number 2143 by 9. So, the 9's complement of the number 2143 is 7856.

9999-2143= 7856

10's Complement

Just like 9’s complement, 10's complement is also used to find the subtraction of the decimal numbers. The 10's complement of a number is calculated by first finding the 9’s complement of the number and then adding 1 in it.

Let us see an example. We have to find the 10’s complement of the given decimal number 2143. For this, we subtract each digit of the number 2143 by 9 to get the 9’s complement. So, the 9’s complement of 2143 is 9999 – 2143 = 7856. Now by adding 1, 7856 +1 =7857, we get 10’s complement.

9999-2143= 7856

7856 + 1 = 7857