GATE CS 2018 Set 1 — Question 43
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumNumber Base ConversionsNumber Systems & ArithmeticDigital Logic
Digital Logic → Number Systems & Arithmetic → Number Base Conversions
Last updated
Question
Consider the unsigned 8-bit fixed point binary number representation below,where the position of the binary point is between and . Assume is the most significant bit. Some of the decimal numbers listed below cannot be represented exactly in the above representation:
(i) 31.500
(ii) 0.875
(iii) 12.100
(iv) 3.001Which one of the following statements is true?
(i) 31.500
(ii) 0.875
(iii) 12.100
(iv) 3.001Which one of the following statements is true?
Correct answer
(C) Only (iii) and (iv) cannot be exactly represented
Solution
The given representation is an unsigned 8-bit fixed point number with the format .
- The integer part consists of 5 bits ( to ). The maximum integer value is .
- The fractional part consists of 3 bits ( to ). The weights are , , and . Any representable fractional part must be a multiple of .
- Integer part: 31. This fits in 5 bits ().
- Fractional part: 0.5. This is a multiple of 0.125 (). It fits in 3 bits ().
- Representation: . Can be represented.
- Integer part: 0. Fits.
- Fractional part: 0.875. This is a multiple of 0.125 (). It fits in 3 bits ().
- Representation: . Can be represented.
- Fractional part: 0.1. This is not a multiple of 0.125 (, which is not an integer). It cannot be represented exactly with 3 fractional bits.
- Cannot be represented.
- Fractional part: 0.001. This is smaller than the resolution (0.125) and not a multiple.
- Cannot be represented.
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…