GATE CS 2025 Set 1 — Question 25
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MSQ+1 / -0EasySigned Number RepresentationsNumber Systems & ArithmeticDigital Logic
Digital Logic → Number Systems & Arithmetic → Signed Number Representations
Last updated
Question
The number can be represented as in 4-bit 2's complement representation. Which of the following is/are CORRECT 2's complement representation(s) of ?
Correct answer
(B) 1111 1010 in 8-bits; (D) 1111 1111 1111 1010 in 16-bits
Solution
In 2's complement representation, to increase the number of bits, we perform sign extension. This means replicating the most significant bit (the sign bit) to the left.
- 4-bit representation: (sign bit is 1).
- 8-bit representation: Extend the sign bit '1' four times to the left . (Option B is correct).
- 16-bit representation: Extend the sign bit '1' twelve times to the left . (Option D is correct).
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CS question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Number Systems & Arithmetic
2026 Set 2 Q16Which one of the following options is not a property of Boolean Algebra? Note: is OR…2026 Set 1 Q21Consider the following Boolean expression of a function :…2026 Set 1 Q22Consider the 8-bit signed integers and represented using the sign-magnitude form. The…2026 Set 2 Q28In a system, numbers are represented using 4-bit two’s complement form. Consider four numbers…2026 Set 2 Q34The 32-bit IEEE 754 single precision representation of a number is . The number…