GATE CS 2026 Set 2 — Question 28
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Digital Logic → Number Systems & Arithmetic → Binary Arithmetic & Overflow
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Question
In a system, numbers are represented using 4-bit two’s complement form. Consider four numbers , , and in the system.
Which of the following operations will result in arithmetic overflow?
Which of the following operations will result in arithmetic overflow?
Correct answer
(B) N2 + N3; (D) N1 + N4
Solution
In 4-bit two's complement representation, the range of representable numbers is from to , i.e., .Let's determine the decimal values of the given numbers:
(A) . This is within the range . No overflow.
(B) . This is less than , so it cannot be represented. Overflow occurs.
(C) . This is within the range. No overflow.
(D) . This is less than , so it cannot be represented. Overflow occurs.Therefore, operations (B) and (D) result in arithmetic overflow.
- . The MSB is 1, so it is negative. Magnitude = 2's complement of . Thus, .
- . MSB is 1. Magnitude = 2's complement of . Thus, .
- . MSB is 1. Magnitude = 2's complement of . Thus, .
- . MSB is 1. Magnitude = 2's complement of . Thus, .
(A) . This is within the range . No overflow.
(B) . This is less than , so it cannot be represented. Overflow occurs.
(C) . This is within the range. No overflow.
(D) . This is less than , so it cannot be represented. Overflow occurs.Therefore, operations (B) and (D) result in arithmetic overflow.
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