GATE | GATE-CS-2006 | Question 85

We consider the addition of two 2’s complement numbers bn-1bn-2…b0 and an-1an-2…a0. A binary adder for adding unsigned binary numbers is used to add the two numbers. The sum is denoted by cn-1cn-2…c0 and the carry-out by cout. Which one of the following options correctly identifies the overflow condition?
(A) A
(B) B
(C) C
(D) D

Answer: (B)

Explanation: Overflow occurs only when two same sign binary numbers added and result of these numbers is different sign in 2’s complement representation.
Otherwise overflow can not be occurred.
Counter example for given options
(A) 0111+0111=1110 has overflow, but given condition violates.
(C) 1001+0001=1010 has no overflow, but given condition violates.
(D) 1111+1111=1110 has no overflow, but given condition violates.

Only option (B) is correct.

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