If A and B are positive numbers calculate AB assuming a ones

If A and B are positive numbers, calculate A-B assuming a one\'s complement number system and n=8; A=101010 and B=1010.

Solution

What is one\'s complement?

It is a number system to store negative values by putting flag(1) in Most Significant Bit(MSB) and complementing the other bits while storing negative numbers. For example,

NOTE: Assuming A and B both as positive numbers as given in the question.

To computer A-B, actually we will be doing A+(-B).

A

+(-B)

1 0 1 0 1 0

1 1 0 1 0 1

42

+(-10)

(011111) + (000001)

= 100000

Step 1: Binary and Decimal value representation of A.

Step 3: Binary and Decimal value representation of B.

Step 3: To do this we change all the 1\'s to 0\'s and 0\'s to 1\'s. Notice that the most-significant digit is now 1 since the number is negative.

Step 4: Re-writing values of A and -B again for better understanding.

Step 5: Performing Binary addition of A and -B. This resulted into overflow bit. In the case of overflow, we have to add 1 to the value.

Step 6: Adjusting overflow value by adding it to the result. Result is 100000.