0380. Show how you would subtract 76 from 35 using both one’s compliment and two’s compliment.

76 = 1001100₂ Or 0000000001001100₂ (On 16-bits)

35 = 100011₂ Or 0000000000100011₂ (On 16-bits)

ONE’S Compliment:

-76 (in one’s compliment) would be:

0000000001001100

↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓

1111111110110011

Subtracting 76 from 35 (35 + -76) would yield:

0000000000100011 (+35)

+ 1111111110110011 (-76)

1111111111010110

NOTE: Since the result is negative, we do not need to add 1. However, we must compliment to make sense of the result:

1111111111010110

↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓

0000000000101001

Check: 0000000000101001₂ = -(32 + 8 + 1) = -41 (correct)

TWO’S Compliment:

-76 (in two’s compliment) would be:

1111111110110011

+ 1

1111111110110100

Subtracting 76 from 35 (35 + -76) would yield:

0000000000100011 (+35)

+ 1111111110110100 (-76)

1111111111010111

Compliment:

1111111111010111

↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓

0000000000101000

And add 1:

0000000000101000

+ 0000000000000001

0000000000101001

Check: 0000000000101001₂ = 25 + 23 = 32 + 8 +1 = 41 (correct)