Question

Let us consider the following equation in a 6-bit binary number system X = A + B A is given as (001010)2 in 1’s complement binary number system, B is given as (111010)2 in signed number system. What would be X in 2’s complement number system?

Answer 1

Binary Addition truth table:

= > 0 + 0 = 0

= > 0 + 1 = 1

= > 1 + 0 = 1

= > 1 + 1 = 0(carry over 1).

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Now,

Given A = (001010)2.

Given B = (111010)2.

Now,

A + B:

= > 0 0 1 0 1 0

= > 1 1 1 0 1 0

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0 1 0 0 0 1 0 0

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Hence,

x = (01000100).

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Now,

Two's complement of X : Add 1 to 1's compliment binary system.

= > (0 1 0 0 0 1 0 0) + (1)

= > 1 0 1 1 1 1 0 0

Therefore, 2's complement of X = (10111100).

Hope this helps!