GATE CS 2019 Set 1 — Question 18
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+1 / -0.33MediumSigned Number RepresentationsNumber Systems & ArithmeticDigital LogicBinary Arithmetic & Overflow
Digital Logic → Number Systems & Arithmetic → Binary Arithmetic & Overflow
Last updated
Question
Consider , where X, Y and Z are all in sign-magnitude form. X and Y are each represented in bits. To avoid overflow, the representation of Z would require a minimum of:
Correct answer
(C) n + 1 bits
Solution
In -bit sign-magnitude representation, 1 bit is for the sign and bits are for the magnitude.
The range of representable values is .Let the maximum positive value be .
The range is .We are computing .
The maximum possible value of occurs when is maximum positive and is minimum negative:
.The minimum possible value of occurs when is minimum negative and is maximum positive:
.So, requires a range of roughly . To represent a magnitude of , we need bits for magnitude (since ). Adding 1 bit for the sign, we need a total of bits.Thus, bits are required to avoid overflow.
The range of representable values is .Let the maximum positive value be .
The range is .We are computing .
The maximum possible value of occurs when is maximum positive and is minimum negative:
.The minimum possible value of occurs when is minimum negative and is maximum positive:
.So, requires a range of roughly . To represent a magnitude of , we need bits for magnitude (since ). Adding 1 bit for the sign, we need a total of bits.Thus, bits are required to avoid overflow.
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…