Half adder

Add two single bits and see the carry pop out. A ready-made arithmetic circuit you can open in the TorchAnvil simulator.

Adding one bit to one bit

When you add two single bits you can get 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, or 1 + 1 = 10 — that last case needs a second bit to hold the carry. A half adder is the smallest circuit that does exactly this: two bits go in, a Sum bit and a Carry bit come out.

How it works

The trick is in the two gates:

• XOR on A and B gives you the Sum bit. XOR is "exactly one is true" — so 1 + 1 correctly rolls back to 0 on the Sum.
• AND on A and B gives you the Carry bit. Carry is only true when both inputs were true — which is the one case Sum alone couldn't represent.

That's why XOR is sometimes called "addition without carry." Bolt an AND beside it to catch the overflow and you've got the real thing.

A	B	Sum	Carry
0	0	0	0
0	1	1	0
1	0	1	0
1	1	0	1

Why it's called "half"

It's a half adder because it can't accept a carry in — only produce one. Wire two half adders together (plus an OR for the carries) and you get a full adder, which is the building block of every multi-bit adder ever built. That's the next sample.

Try this

• Flip both levers on. The Sum lamp goes dark and the Carry lamp lights — you've just witnessed 1 + 1 = 10 in silicon.
• Flip only one. Sum lights, Carry stays dark — 0 + 1 = 01.