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)