What is the difference between a half adder and a full adder?

A half adder adds two single bits producing a sum and carry output (Sum = A XOR B, Carry = A AND B). It cannot handle carry input from previous stage. A full adder adds three bits (two inputs plus carry-in) producing sum and carry-out (Sum = A XOR B XOR Cin, Cout = AB + Cin(A XOR B)). Full adders are cascaded to create multi-bit ripple carry adders, where each carry-out connects to the next carry-in.