Your first adder

Two inputs, two outputs. You're officially doing arithmetic now. Build a half adder — the circuit that adds two bits and reports the carry.

What you'll learn

• How binary addition works bit-by-bit: 0+0=0, 1+1=10 (that's a carry).
• Why a one-bit adder needs two outputs, not one.
• How to combine the gates you already know into a tiny calculator.

The idea

Adding two single-bit numbers has four cases:

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

That last row is the interesting one: 1 + 1 = 10 in binary. So our adder has to produce two outputs — the current digit (Sum) and the overflow into the next column (Carry).

The trick: Sum is exactly an XOR of A and B, and Carry is exactly an AND of A and B. Two gates, one bit of addition.

The challenge

Place two Levers labeled Input A and Input B. Place two Lamps labeled Sum and Carry. Wire them through:

• an XOR gate → the Sum lamp
• an AND gate → the Carry lamp

Flip through all four lever combinations and confirm the lamps match the table above.

Where this leads

One half adder handles the two least-significant bits. Stack two half adders (with one extra OR) and you get a full adder — the building block that lets you add any two binary numbers, one column at a time. Every CPU ever made has that circuit buried inside it.