10's complement subtraction steps :
1. find 10's complement of the subtrahend.
2. Then add it to the minuend.
3. If the final carry over of the sum is 1, then it is dropped and the result is positive.
4. If there is no carry over, then 10's complement of the sum is the final result and it is negative.
The radix complement of an n digit number x in radix r can be defined as (r^n – x). Alternatively we can obtain by adding 1 to the diminished radix complement. (Diminished radix complement = (r^n – 1) – x).
10’s complement → 9’s complement of the no. + 1
a.) 5250 – 1321
10’s complement of 1321 → 9’s complement of 1321 + 1 → 9999 – 1321 = 8678 +1 = 8679
Add it to the minuend → 5250 + 8679 = 13929
Discard the carry → Result = 3929
b.) 9753 – 8640 → 9’s complement of 8640 + 1 → 9999 – 8640 = 1359 + 1 = 1360
9753 + 1360 = 11113
Discard the carry → Result = 1113
c.) 20 – 100
10’s comp of 100 → 999 – 100 = 899 + 1 = 900
Add 20 + 900 = 920
No carry, find 10’s comp of the above sum → 999 – 920 = 79 + 1 = 80
Result = -80.
d.) 1200 – 250
10’s comp of 250 → 9999 – 0250 = 9749 + 1 = 9750
Add it to 1200 → 1200+9750 = 10950
Discard the carry → 0950 , Result = 950.
