Identify “one-or-the-other” logic Which logic circuit outputs HIGH if one input or the other input, but not both, is HIGH?
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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-OR gate
Explanation
Introduction / Context:Sometimes we require a signal that indicates exclusivity: exactly one of two conditions is true. The exclusive-OR (XOR) gate implements this function at the 1-bit level and is widely used in arithmetic and parity generation.
Given Data / Assumptions:
- Two inputs A and B.
- Desired behavior: X = 1 when A ≠ B; X = 0 when A = B.
Concept / Approach:The XOR truth table is 1 for input pairs 01 and 10, and 0 for 00 and 11. This matches “one or the other, but not both.”
Step-by-Step Solution:
List cases: A=0,B=0 → X=0; A=0,B=1 → X=1.A=1,B=0 → X=1; A=1,B=1 → X=0.Therefore XOR provides the exclusive condition.Other common gates (OR, NAND, XNOR) do not satisfy exclusivity.Verification / Alternative check:Boolean identity: X = A XOR B = (A + B) * (NOT(A*B)). It is OR gated with the complement of AND, ensuring not both.
Why Other Options Are Wrong:
- Ex-NOR: True for equality (both same), opposite of exclusivity.
- OR: True for 11 as well, violating “not both.”
- NAND: False only when both are 1; not the exclusive function.
Common Pitfalls:Assuming OR implies exclusivity; OR includes the both-true case, whereas XOR excludes it.
Final Answer:Ex-OR gate