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Digital Arithmetic Operations and Circuits - Technical MCQs

Q1:

The 2's-complement system is to be used to add the signed binary numbers 11110010 and 11110011. Determine, in decimal, the sign and value of each number and their sum.

A –113 and –114, –227

B –14 and –13, –27

C –11 and –16, –27

D –27 and –13, –40

ANS:B - –14 and –13, –27

When we complement 11110010 for 1's complement, we get 00001101. Then add 1 in 1's complement to get 2's complement.

00001101+1 =00001110.

The decimal of 00001110 is 14. And the sign of the number is "-" because in 11110010, the starting number is "1". So, the number is -14.

Similarly the 2's complement of 2nd number is 00001101, and we get 13 as decimal value. The sign of the number is again negative as we can see "1" as MSB, so the number in decimal is -13.

When we add the 2's complement of both numbers, we get 27 as total decimal value and the sign is negative, because both the numbers were negative.