9's and 10's Complement

What is 9’s complement?

9’s complement of any Decimal number is obtained by subtracting each digit of given number by 9. Like 1’s complement 9’s complement is also used to subtract the number using addition. 

Example:

Find the 9’s complement of 2592.

Solution:

9’s complement of 2592  = 9 9 9 9 – 2 5 9 2                            

                                        =7 4 0 7

What is 10’s complement?

10’s complement of any Decimal number is the sum 1 to its 9’s complement. It is just like 2’s complement in binary number representation. Example:

Find the 10’s complement of 2592.

Solution:

10’s complement of 2592  = 9’s complement of 2592 +1

(9 9 9 9 - 2 5 9 2) + 1                           

                                                = 7 4 0 8

           

Subtraction Using 9’s and 10’s complement

i)                    288 - 52

Solution:

Subtraction using 9’s Complement

Making equal number of digits in both number

   288 (minuend)

-  052 (by inserting 0 to the left side of subtrahend)

9’s complement of 052 (Subtrahend)

= 9 9 9 – 0 5 2

= 9 4 7

Add both number (minuend and the 9’s complement of subtrahend)

   2 8 8

+ 9 4 7

1 2 3 5

Hence, there is carry digit, so answer is positive and sum of carry digit and it’s remaining part. (1+235)

Therefore, final result is 236.

Subtraction using 10’s Complement

i)                    288 - 52

Making equal number of bits in both number

   288

-  052 (by inserting 0 to the left side of subtrahend)

10’s complement of 052 (Subtrahend)

= 9’s complement of 052 + 1

= (9 9 9 - 0 5 2) + 1

= 9 4 7 + 1 = 9 4 8

Add both number (minuend and the 10’s complement of subtrahend)

   2 8 8

+ 9 4 8

1 2 3 6

Hence, there is carry digit, so answer is positive and remaining part ignoring carry digit.

Therefore, final result is 236.