Skip to content
GATEiit

GATE CSE 2022 Q18: Which 4-bit 2's complement addition overflows

Question

Let R1 and R2 be two 4-bit registers that store numbers in 2's complement form. For the operation R1+R2, which one of the following values of R1 and R2 gives an arithmetic overflow?

Try it: multiple choice: exactly one correct option

Select one option
Wrong answer costs 1/3 mark in GATE.
Show answer and explanation

Answer: B (official GATE 2022 final answer key)

Concept used: 4-bit 2's complement holds −8-8 to 77; overflow happens when the true sum falls outside that range.

First step: Convert each pair to decimal (e.g. 1100=−41100 = -4, 1010=−61010 = -6) and check whether the sum lies in [−8,7][-8, 7].

Full step-by-step solution

Detailed working, common mistakes and linked mock tests will be available with a free GATEiit account. Log-in is coming soon.

Share this question

WhatsAppDownload image

Source: official GATE 2022 CS question paper and final answer key, organised by IIT Kharagpur. Question paper · Answer key

More Digital Logic PYQs

PracticePractise Digital Logic questions →Full paperAll GATE CSE 2022 questions →