Discussion
The correct circuit of a Half Adder is :
- A.
- B.
- C.
- D.
Answer: B
The correct half adder is circuit (B): an XOR gate gives the sum S and an AND gate gives the carry C.
A half adder adds two single bits A and B. The truth table is 0+0 = 00, 0+1 = 01, 1+0 = 01 and 1+1 = 10, written as carry and sum. The sum bit is 1 only when exactly one input is 1, which is A XOR B. The carry bit is 1 only when both inputs are 1, which is A AND B:
\[ S = A \oplus B \]
\[ C = A \cdot B \]
Circuit (A) swaps the two gates, so it gives the wrong sum and carry. Circuit (C) uses an OR gate for the sum, which gives 1 for 1+1 where the sum should be 0. Circuit (D) uses NAND and NOR gates, which are the complements of AND and OR, so it is not an adder either.
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