Exam-style question
Try this first
Construct the truth table for a half-adder. Give Boolean expressions for the Sum and Carry outputs, and describe the logic gate circuit needed to construct it.
Model answer
What a good answer should say
- A half-adder has two inputs, A and B, and two outputs, Sum and Carry.
- The truth table is: A=0, B=0 gives Sum=0, Carry=0; A=0, B=1 gives Sum=1, Carry=0; A=1, B=0 gives Sum=1, Carry=0; A=1, B=1 gives Sum=0, Carry=1.
- The Boolean expressions are Sum = A XOR B and Carry = A AND B.
- The circuit uses the same two inputs in parallel: connect A and B to an XOR gate to produce Sum, and connect A and B to an AND gate to produce Carry.
Explanation
Why this works
The Sum output is 1 when exactly one input is 1, which is the behaviour of XOR. The Carry output is 1 only when both inputs are 1, which is the behaviour of AND.
Common mistake
No common mistake is linked to this question yet.