Half Adder
A half adder adds two one-bit numbers, A and B, and gives a two-bit answer: a Sum and a Carry. It is the smallest adder there is, and the first step towards adding numbers of any width.
Try it live
This is the Circuit Simulator itself, running in the page — it is LogicsBench's own example design, read-only. Open it full size, and sign in to make your own copy to change.
- Flip A and B on the switch bank and watch the two outputs.
- Set both to 1: Sum goes to 0 and Carry to 1 — binary 10, which is two.
- Open the Truth table tab to see all four rows at once.
Half adder truth table
| A | B | Sum | Carry |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
How it works
Sum = A ⊕ BCarry = A · B
Sum is 1 when exactly one input is 1 — that is the exclusive OR (XOR) of A and B.
Carry is 1 only when both inputs are 1 — the AND of A and B. 1 + 1 is binary 10: a sum of 0 and a carry of 1.
It cannot take a carry in from a previous column, which is why adding numbers wider than one bit needs a full adder.
Building it from 74-series chips
Built from NAND gates alone it takes five: a 74LS00 and one gate of a second.