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GATE CSE 2026 Session 2 Q28: Overflow in 4-bit two's complement additions

Question

In a system, numbers are represented using 4-bit two's complement form. Consider four numbers N1=1011N_1 = 1011, N2=1101N_2 = 1101, N3=1010N_3 = 1010 and N4=1001N_4 = 1001 in the system.

Which of the following operations will result in arithmetic overflow?

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Answer: B, D (official GATE 2026 final answer key)

Concept used: 4-bit two's complement holds −8 to 7; overflow occurs when the true result is outside this range.

First step: Decode the numbers: N1=−5N_1 = -5, N2=−3N_2 = -3, N3=−6N_3 = -6, N4=−7N_4 = -7, then compute each result.

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Source: official GATE 2026 Session 2 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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