EASA Part-66 · Module 5 — 5.3 Logic Circuits · B1/B2

Half Adder & Full Adder

Objective: describe how XOR and AND gates form a half adder, how a full adder adds a carry-in, and how full adders chain to add multi-bit numbers.

Adder logic

Sum

Carry out

Truth table

Adding two bits gives a Sum and a Carry. A half adder uses one XOR (sum) and one AND (carry). A full adder also takes a carry-in, so it can be chained to add multi-bit numbers — the carry-out of one stage feeds the carry-in of the next. Sum = A XOR B XOR Cin; Carry-out is high when two or more inputs are high.

Try this: Half adder: set A=1, B=1. Why is the sum 0 with a carry of 1?
Try this: Switch to full adder. Set A=1, B=1, Cin=1. Read sum and carry — what binary number is that?
Try this: Explain how stacking full adders lets you add two 8-bit numbers.