A Half Adder

This lesson builds step by step toward a half adder — a circuit that can add two binary digits.

Step 1

AND → NOT = NAND

Feed the output of an AND gate into a NOT gate. Output is only 0 when both inputs are 1.

AND

A	B	AND	Q (NAND)
0	0	0	1
0	1	0	1
1	0	0	1
1	1	1	0

Step 2

OR → NOT = NOR

An OR gate followed by a NOT. Output is 1 only when both inputs are 0.

A	B	OR	Q (NOR)
0	0	0	1
0	1	1	0
1	0	1	0
1	1	1	0

Step 3

AND + OR (three inputs)

A and B feed an AND gate. That result, plus a third input C, feed an OR gate. Q = (A AND B) OR C.

A·B

A	B	C	A·B	Q
0	0	0	0	0
0	0	1	0	1
0	1	0	0	0
0	1	1	0	1
1	0	0	0	0
1	0	1	0	1
1	1	0	1	1
1	1	1	1	1

Step 4 — the key insight

XOR + AND = half adder

Two inputs, two gates in parallel, two outputs. XOR gives the Sum bit. AND gives the Carry bit.

Why two outputs? Adding 1+1 in binary gives 10 — two digits. Sum is the right digit, Carry is the left. Try it: set both A and B to 1. Sum=0, Carry=1 — that's binary 10, which equals decimal 2.

Sum

Carry

A	B	Sum (XOR)	Carry (AND)	Decimal
0	0	0	0	0+0 = 0
0	1	1	0	0+1 = 1
1	0	1	0	1+0 = 1
1	1	0	1	1+1 = 2

Next lesson: Full Adder

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