Equality detection: Which gate provides a HIGH output exactly when its two inputs have equal logic levels (both 0 or both 1)?
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AXOR gate
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BXNOR gate
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CNAND gate
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DNOR gate
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EAND gate
Answer
Correct Answer: XNOR gate
Explanation
Introduction / Context:Comparing two binary signals is a common task. The equality function outputs HIGH when inputs match. Recognizing which primitive gate directly implements equality simplifies design work for comparators and parity logic.
Given Data / Assumptions:
- Two-input standard logic gates under positive logic.
- Goal is equality detection (A = B).
Concept / Approach:By definition, XOR is HIGH when inputs differ; therefore its complement, XNOR, is HIGH when inputs are equal. The XNOR truth table places 1s at (0,0) and (1,1) and 0s at (0,1) and (1,0).
Step-by-Step Solution:
Recall XOR identity: XOR = A′B + AB′ (different).XNOR = (XOR)′ = A′B′ + AB (equal).Thus, for equality detection, choose XNOR.No additional logic is required for the two-input case.Verification / Alternative check:Build a small truth table or evaluate A′B′ + AB for all four input pairs; outputs are 1 only on equality rows, confirming XNOR.
Why Other Options Are Wrong:
- XOR: Detects inequality.
- NAND/NOR/AND: Do not implement equality; their truth tables do not match equality-only HIGH behavior.
Common Pitfalls:Confusing XOR with XNOR; attempting to build equality with AND/OR and inverters when a single XNOR suffices.
Final Answer:XNOR gate