Exam-style question
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Design a circuit that outputs 1 only when exactly two of the three inputs A, B, C are 1.
- A.XOR gate between A and B, then AND with C.
- B.Majority gate.
- C.XOR gate between A and B, then OR with C.
- D.AND gate between A and B, then OR with C.
Model answer
What a good answer should say
- XOR gate between A and B, then AND with C.
Explanation
Why this works
Formula/rule: Boolean expression decomposition. Substitution: F = (A·B·C') + (A·B'·C) + (A'·B·C).
Working: XOR(A,B) gives 1 when exactly one of A,B is 1; AND with C gives 1 when C=1 and exactly one of A,B is 1, i.e., exactly two of the three inputs are 1. Answer: XOR gate between A and B, then AND with C.
Conclusion: This circuit outputs 1 only when exactly two inputs are 1.
Common mistake
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