GATE EC 2022 Set 1 — Question 49
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MSQ+2 / -0HardBoolean Algebra & IdentitiesCombinational LogicDigital Circuits
Digital Circuits → Combinational Logic → Boolean Algebra & Identities
Last updated
Question
Consider a Boolean gate (D) where the output is related to the inputs and as, , where denotes logical OR operation. The Boolean inputs ‘0’ and ‘1’ are also available separately. Using instances of only D gates and inputs ‘0’ and ‘1’, __________ (select the correct option(s)).
Correct answer
(A) NAND logic can be implemented; (C) NOR logic can be implemented
Solution
The given Boolean gate D performs the operation .
1.NOT Gate Implementation: By setting the input , the output becomes . Thus, a NOT gate can be implemented using one D gate and the constant input '0'.
2.OR Gate Implementation: Since we can implement a NOT gate, we can obtain from . By passing and as inputs to another D gate, the output is . Thus, an OR gate can be implemented using two D gates.
3.Functional Completeness: A set of gates that can implement both NOT and OR is functionally complete. This means any Boolean function can be realized using only these gates.
- Since the set {NOT, OR} is functionally complete, NAND and NOR logic can definitely be implemented.
- Therefore, options (A) and (C) are correct.
- Options (B) and (D) are incorrect because OR and AND (derived from NOT and OR via De Morgan's laws) can indeed be implemented.
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 ?