Half Adder and Full Adder

A half adder adds two single bits. It produces a sum bit and a carry bit: 1 + 1 is 2, which is 10 in binary, so the sum bit is 0 and the carry bit is 1. A half adder has no way to accept a carry coming in from a lower position, which is why it is only half the story.

A full adder adds three bits: two data inputs plus a carry-in from the previous position. It produces a sum bit and a carry-out. The sum bit is 1 when an odd number of the three inputs are 1 (an exclusive-or of all three). The carry-out is 1 whenever at least two of the three inputs are 1.

The full adder matters because it composes. Chain full adders so that each one's carry-out feeds the next one's carry-in, and you can add numbers of any width. That is exactly how the ripple-carry adder in the next lesson is built.