Reference

The logic gates

A gate takes one or two inputs, each on (1) or off (0), and gives one output. Six gates build everything a computer does. The little table under each gate is its truth table — it shows the output for every possible input. Back to the lab anytime: Open the circuit lab →

• AND &

  On only when BOTH inputs are on. Think "a and b are both true".

  a	b	out
  0	0	0
  1	0	0
  0	1	0
  1	1	1

• OR ≥1

  On when AT LEAST ONE input is on. Off only when both are off.

  a	b	out
  0	0	0
  1	0	1
  0	1	1
  1	1	1

• NOT ¬

  Flips one input: on becomes off, off becomes on. The only one-input gate.

  a	b	out
  0	—	1
  1	—	0

• XOR =1

  On when the two inputs are DIFFERENT (exactly one is on). This is the "sum" bit of adding.

  a	b	out
  0	0	0
  1	0	1
  0	1	1
  1	1	0

• NAND &̄

  AND, then flipped — off only when both inputs are on. Every other gate can be built from just NAND.

  a	b	out
  0	0	1
  1	0	1
  0	1	1
  1	1	0

• NOR ≥1̄

  OR, then flipped — on only when both inputs are off.

  a	b	out
  0	0	1
  1	0	0
  0	1	0
  1	1	0

Adding two bits needs just two gates: the sum is a XOR b and the carry is a AND b. Chain those and you have built an adder — the heart of a CPU. Try a challenge →