GATE EC 2026 Set 1 — Question 56
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MSQ+2 / -0MediumK-Map MinimizationCombinational LogicDigital CircuitsCanonical SOP & POS
Digital Circuits → Combinational Logic → Canonical SOP & POS
Last updated
Question
Consider the four-variable Boolean function,with '' as MSB and '' as LSB. Which of the following expressions is/are the valid form(s) of ?
Correct answer
(A) xz + xz + wxy; (D) xz + xz + wyz
Solution
The Boolean function is given by .
1.Minterm Analysis:
The minterms are .2.K-map Grouping:
- The four corners form a quad representing .
- The minterms form a quad representing .
- The remaining minterm is .
- can be combined with to form the prime implicant .
- Alternatively, can be combined with to form the prime implicant .
- Option (A): . This covers all minterms correctly. Valid.
- Option (B): . Note that . Thus, this expression is equivalent to Option (A). Valid.
- Option (C): . The term corresponds to , which is not a minterm of . Also, it misses . Invalid.
- Option (D): . This covers all minterms correctly (using the alternative grouping for ). Valid.
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 ?