The half adder: adding two bits
Computers add numbers in binary, one bit at a time. The half adder is the circuit that adds two single bits, A and B. Because 1 + 1 = 2, which is 10 in binary, it needs two outputs: the sum bit S and the carry bit C.
Truth table
| A | B | S | C |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
Try it Click the inputs to change them.
S0C0
How it works
Write out the four cases: 0 + 0 = 00, 0 + 1 = 01, 1 + 0 = 01 and 1 + 1 = 10. Now look at each output column on its own. S is 1 when exactly one input is 1: that is an XOR gate. C is 1 only when both inputs are 1: that is an AND gate. So a half adder is just two gates side by side.
It is called “half” because it can’t accept a carry coming from the previous column. Adding that third bit is the job of the full adder.
Hints and solution
Try on your own first. Each hint gives away a little more.
- 1 + 1 = 10 in binary: S = 0, C = 1.
- S is 1 when exactly one input is 1. C is 1 when both are.