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If A and B are the inputs of a half adder, then the sum is given by __________

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Answer & Explanation

Correct AnswerC. A XOR B

Quick Explanation

A half adder adds two single-bit inputs. Its Sum output is 1 only when A and B are different, which is exactly the XOR truth table; the Carry output is A·B.

Formula / Key Relation

Sum S = A ⊕ B

Carry C = A·B

Detailed Explanation

Concept & Reasoning

For inputs 00, 01, 10, 11, the binary sums are 0, 1, 1, 10. Hence the Sum bit sequence is 0,1,1,0 = A ⊕ B, while the Carry is 0,0,0,1 = AB. This is one of the basic identities used to build a full adder.

How to Solve It in the Exam

Half adder: XOR for Sum, AND for Carry.

Important Exam Point

Memorize the pair together; exam distractors often swap Sum and Carry.

Related Revision Path

This question sits in the revision path Digital Electronics → Combinational Logic → Adders .

Quick Trick

Half adder: XOR for Sum, AND for Carry.

Common Mistake

Selecting OR for Sum; OR fails for A=B=1 because the correct sum bit is 0 with carry 1.

Exam Tip

Memorize the pair together; exam distractors often swap Sum and Carry.

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Exam Path

Knowledge Path

Study concept · Half Adder Sum →Practice concept Practice topic

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