Question

Subtract the following decimal numbers by the 9’s and 10’s complement methods. i) 274 - 86 ii) 93 - 615 iii) 574.6 - 297.7 iv) 376.3 - 765.6

Answer 1

1. 188

2.-522

3.276.9

4.-386.3

Hope You find useful

S.Harish Abhimanyu

Answer 2

In 9’s complement method, a number can be converted into 9’s complement by subtracting the number from (10^n -1) where n is number of digits in the number(max of both).  

To get 10’s complement of the above 9’s complement number, just add 1.  This 1 is adjusted to left most digit.  

To subtract 2 numbers using 9’s complement and 10’s compliment we need to do as follow.

A – B using 9’s complement  

Step 1: Get the 9’s complement of B.  

Step 2: Add A to above number

Step 3: Convert the result into 10’s complement.  

If there is a carry forward, it is negative number. And converting into 10’s complement is to subtract (10^n -1) – above step 2 result.  

If there is no carry forward, it is positive number. Converting 10’s complement is by removing carry forward and +1 to step 2.  

i. 274 – 86 using 9’s and 10’s complement.  

9’s complement of 86 = (1000 – 1) – 86 = 913.

Add 274 above number, 274 + 913 = 1187.

Convert 1187 into 10’s complement by adding + 1 and adjust carry forward.  

= 187 + 1 = 188  

= 188 (Since there is carry forward, remove left most digit and add to remaining number.)

Hence 274 – 86 = 188.  

ii. 93 – 615 using 9’s and 10’s complement.  

9’s complement of 615 = (1000 – 1) – 615 = 384.

Add 93 above number, 93 + 384 = 477.

Convert into 10’s complement. (Since there is no carry forward, it is negative number. And subtract from 999)

= 999 - 477 = 522

Hence 93 – 615 = -522  

iii. 574.6 - 297.7 using 9’s and 10’s complement.

For decimal number, ignore decimal while calculation and add it at the same position.  

9’s complement of 297.7 = (1000 – 0.1) – 297.7 = 999.9 – 297.7 = 702.2

Add 574.6 to above number, 702.2 + 574.6 = 1276.8

Convert into 10’s complement. (Since there is carry forward, take the left most and add to remaining number.)

= 276.8 + 0.1 = 276.9

574.6 – 297.7 = 276.9

iv. 376.3 - 765.6  

9’s complement of 765.6 = 999.9 – 765.6 = 234.3

Add 376.3 to above number, 376.3 + 234.3 = 610.6

Convert to 10’s complement. (Since there is no carry forward, it is negative number and subtract the number from 999.9)

999.9 – 610.6 = 389.3  

376.3 - 765.6 = -389.3