A half adder adds two one-bit operands and produces a sum and carry. A full adder adds those operands plus a carry-in. The sum is the low bit of the total; the carry is its high bit. Full adders can be chained to add wider words.
Worked example
For A = 1, B = 1 and carry-in = 1, the total is decimal 3, or binary 11. The full adder therefore produces sum = 1 and carry-out = 1. Its equations are sum = A XOR B XOR Cin and Cout = AB + ACin + BCin.
What to watch for
A half adder has no carry-in, so it cannot directly replace every stage of a multi-bit carry chain.
Try it yourself
What does a half adder produce for inputs 1 and 1?
Answer: Sum = 0 and carry = 1, because binary 1 + 1 = 10.
How to study this topic
State the operand width and signedness first. Work out a decimal answer, then compare it with the binary result. Keep result bits, carry, borrow and signed overflow distinct when interpreting the circuit's output.
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Digital Electronics