Identify the equality gate Which logic gate outputs HIGH when both inputs are HIGH or both inputs are LOW (i.e., when the inputs are equal)?
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AEx-NOR gate
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BOR gate
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CEx-OR gate
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DNAND gate
Answer
Correct Answer: Ex-NOR gate
Explanation
Introduction / Context:Digital systems frequently need to compare two signals. The gate that outputs HIGH when the inputs are the same implements equality at the 1-bit level and is commonly used in comparators and parity circuits.
Given Data / Assumptions:
- Two binary inputs A and B.
- We seek a gate that asserts when A equals B (00 or 11).
Concept / Approach:The exclusive-NOR (XNOR) function is 1 exactly when inputs match. Boolean form: X = A*B + A'B'. This is the complement of XOR, which is 1 when inputs differ.
Step-by-Step Solution:
Evaluate truth table pairs: 00 → 1, 01 → 0, 10 → 0, 11 → 1.This matches the equality condition.Therefore, the equality gate is XNOR.Other common gates (OR, NAND) do not meet this pattern.Verification / Alternative check:Construct XNOR from simpler gates: two ANDs (AB and A'*B') feeding an OR implements equality, confirming the behavior.
Why Other Options Are Wrong:
- OR gate: Produces 0 only for 00; does not assert for 11 exclusively.
- Ex-OR gate: Asserts when inputs differ (01 or 10).
- NAND gate: Produces 0 only for 11; not an equality detector.
Common Pitfalls:Confusing XOR with XNOR because of similar names; remember XNOR is the complemented XOR and corresponds to equality.
Final Answer:Ex-NOR gate