Topic 10 · Boolean logic
Logic gates and truth tables
The six logic gates, NOT, AND, OR, NAND, NOR, and XOR, with their symbols and truth tables.
Lesson 1 of 2Syllabus 10.1, 10.2updated October 31, 2026
Gates make decisions with 1s and 0s
A logic gate is an electronic component that takes one or two binary inputs and produces one binary output. 1 means on (TRUE), 0 means off (FALSE). Every calculation a CPU does is built from millions of these gates.
A truth table lists every possible combination of inputs and the output for each. With 2 inputs there are 4 rows; with 3 inputs there are 8.
Try every gate
Pick a gate, then click the inputs (or a row of the truth table). Highlighted wires carry a 1.
Logic gate explorerInteractive
| A | Out |
|---|---|
| 0 | 1 |
| 1 | 0 |
Click an input or a table row.
The rules in words
| Gate | Output is 1 when... | Expression |
|---|---|---|
| NOT | the input is 0 (it flips the input) | X = NOT A |
| AND | both inputs are 1 | X = A AND B |
| OR | at least one input is 1 | X = A OR B |
| NAND | NOT AND: the inputs are not both 1 | X = A NAND B |
| NOR | NOT OR: neither input is 1 | X = A NOR B |
| XOR | the inputs are different | X = A XOR B |
Exam tip. A small circle (bubble) on a gate's output means NOT. That is the only difference between AND and NAND, or OR and NOR.
Key terms
- Logic gate
- A component that performs a Boolean operation on binary inputs.
- Truth table
- A table showing the output for every combination of inputs.
- XOR
- Exclusive OR: outputs 1 only when the inputs are different.
Check yourself
Which gate outputs 0 only when both inputs are 1?Show answer
NAND.
What is 1 XOR 1?Show answer
0: the inputs are the same.
How many rows does a truth table with 3 inputs need?Show answer
2³ = 8 rows.