Reference chart

Logic gate truth tables

Print it: Logic gates cheat sheet (PDF: A4 · US Letter)

A logic gate follows one fixed rule, and its truth table lists that rule in full: one row for every way the inputs can be set. Here are all seven gates, how to write each one, and the chips that hold them.

The seven gates

Gate	Written	Output is 1 when	Use it for
NOT	Ā	the input is 0	Flipping a signal
AND	A · B	every input is 1	All conditions at once: a two-hand safety press
OR	A + B	any input is 1	Any one condition: a car's courtesy light
NAND	NOT(A · B)	any input is 0	Building any other gate
NOR	NOT(A + B)	every input is 0	"Nothing is on": every door shut
XOR	A ⊕ B	the inputs differ	Stair lights switched from either end, adding bits
XNOR	NOT(A ⊕ B)	the inputs match	Checking two bits are equal

In logic, + means OR, not adding, so 1 + 1 = 1.

NOT

A NOT gate, also called an inverter, has one input and flips it.

A	NOT A
0	1
1	0

AND, OR and XOR

A	B	AND	OR	XOR
0	0	0	0	0
0	1	0	1	1
1	0	0	1	1
1	1	1	1	0

NAND, NOR and XNOR

A bubble on a gate's output is a NOT, so each of these is the gate above with every answer flipped.

A	B	NAND	NOR	XNOR
0	0	1	1	1
0	1	1	0	0
1	0	1	0	0
1	1	0	0	1

Three inputs

With three inputs there are eight rows. AND gives 1 only on the last row, OR gives 0 only on the first, and XOR gives 1 when an odd number of inputs are 1.

A B C	AND	OR	XOR
0 0 0	0	0	0
0 0 1	0	1	1
0 1 0	0	1	1
0 1 1	0	1	0
1 0 0	0	1	1
1 0 1	0	1	0
1 1 0	0	1	0
1 1 1	1	1	1

Gate chips

Each chip holds several identical gates with two inputs each, except the inverters. 74HC chips run from 2 to 6 V, so 3.3 V and 5 V boards both suit them; 4000-series chips run from 3 to 18 V.

Gate	74HC chip	4000-series chip	Gates in a chip
NOT	74HC04	4069	Six
NOT, Schmitt trigger	74HC14	40106	Six
AND	74HC08	4081	Four
OR	74HC32	4071	Four
NAND	74HC00	4011	Four
NOR	74HC02	4001	Four
XOR	74HC86	4070	Four
XNOR	74HC7266	4077	Four

The 74HC00, 74HC08, 74HC32 and 74HC86 share one pinout, but the 74HC02 is wired differently: its outputs come first. Check the datasheet before you swap one chip for another.

Using the tables

Find the inputs and write the rule in words, with "and", "or" and "not".
Turn each word into a gate, with brackets for the order: LIGHT = (DARK · MOTION) + SWITCH.
Check every row of the truth table against what you wanted.

Free lesson

Now build it yourself

Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.

Try it yourself: free lesson

“Logic gates” is lesson 2 of 6 in Logic Grid, Electronics World 7. Free with an account. Lessons unlock in order, so you’ll do the 43 before it first.

Or start from the very first lesson, no account needed

Work it out

Binary, decimal and hex converterDecimal, binary and hex, with every bit's place value added up.

The ideas behind it

Questions people ask

What is the difference between OR and XOR?

They differ only when both inputs are 1. OR gives 1 there, because at least one input is on. XOR gives 0, because it wants the inputs to differ: one or the other, but not both.

Which logic gates are universal?

NAND and NOR. Each one alone can build every other gate: a NAND with its inputs tied together is a NOT, a NAND then a NOT is an AND, and three NANDs make an OR. That's why chips can be made from NAND cells alone.

Which chip has NAND gates?

The 74HC00 holds four 2-input NAND gates in a 14-pin package, and runs from 2 to 6 V. Its CMOS 4000-series cousin is the 4011, which runs from 3 to 18 V.

How many rows does a truth table have?

One for every way the inputs can be set: 2ⁿ rows for n inputs. A two-input gate has four rows, a three-input gate eight, and a four-input gate sixteen.