GATE EC 2017 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 / -0.67EasyCanonical SOP & POSCombinational LogicDigital CircuitsK-Map Minimization
Digital Circuits → Combinational Logic → Canonical SOP & POS
Last updated
Question
Which one of the following gives the simplified sum of products expression for the Boolean function , where and are minterms corresponding to the inputs A, B and C with A as the MSB and C as the LSB?
Correct answer
(B) A C + AB + ABC
Solution
The given Boolean function is .
The inputs are A, B, and C, with A as the Most Significant Bit (MSB) and C as the Least Significant Bit (LSB).The minterms are:
We can form groups of 1s:
.This matches option (B).
The inputs are A, B, and C, with A as the Most Significant Bit (MSB) and C as the Least Significant Bit (LSB).The minterms are:
- (for input 000)
- (for input 010)
- (for input 011)
- (for input 101)
| BC=00 | BC=01 | BC=11 | BC=10 | |
|---|---|---|---|---|
| A=0 | 1 | 0 | 1 | 1 |
| A=1 | 0 | 1 | 0 | 0 |
1.A group of two 1s at and . This covers and . The common term is .
2.A group of two 1s at and . This covers and . The common term is .
3.A single 1 at , which is . This cannot be grouped with any other adjacent 1.
The simplified Sum of Products (SOP) expression is the sum of these terms:.This matches option (B).
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 EC 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 Combinational Logic
2026 Set 1 Q20In the circuit shown in the Figure, A and B are logic inputs and Y is the logic output. Which of…2026 Set 1 Q27A binary ripple counter is designed to count to . Which of the following…2026 Set 1 Q35The negative edge triggered JK flip-flop in the Figure has J and K inputs tied to Logic High and a…2026 Set 1 Q42The address of the first location of a 256 kilo byte (KB) memory is . Choose the correct…2026 Set 1 Q45What is the complement of ?