22 min read

AND, OR and NOT Gates

The three basic gates: their symbols, truth tables, Boolean expressions and everyday meanings.

The AND Gate

An AND gate gives 1 only when all its inputs are 1 . If any input is 0, the output is 0. Boolean expression: Q = A \cdot B — read "Q equals A AND B". The dot means AND. Some books write it as AB with no dot.

The AND gate

Q = 0

Output is 1 only when every input is 1.

$Boolean expression: Q = A \cdot B$

Try it:

Press A and B to switch them on and off, or click a row of the truth table.

An OR gate gives 1 when at least one input is 1 . The output is 0 only when every input is 0. Boolean expression: Q = A + B — read "Q equals A OR B". Here + means OR, not addition.

The OR gate

Q = 0

Output is 1 when at least one input is 1.

$Boolean expression: Q = A + B$

Try it:

Find the only row where the output is 0.

A NOT gate (also called an inverter) has one input . It outputs the opposite : 0 becomes 1 and 1 becomes 0. Boolean expression: Q = A — read "Q equals NOT A". The bar over the letter means NOT. You may also see A' or \negA . The small circle (the bubble) on the symbol always means NOT.

The NOT gate

Q = 1

A	Q
0	1
1	0

Output is the opposite of the input.

$Boolean expression: Q = A$

Try it:

Toggle A and watch the output flip.

Truth tables for AND, OR (two inputs) and NOT
Truth tables for AND, OR (two inputs) and NOT

Practice

For a 2-input OR gate, in how many of the 4 rows is the output 1?

The AND Gate

An AND gate gives 1 only when all its inputs are 1 . If any input is 0, the output is 0. Boolean expression: Q = A \cdot B — read "Q equals A AND B". The dot means AND. Some books write it as AB with no dot.

The AND gate

Q = 0

Output is 1 only when every input is 1.

$Boolean expression: Q = A \cdot B$

Try it:

Press A and B to switch them on and off, or click a row of the truth table.

The OR Gate

An OR gate gives 1 when at least one input is 1 . The output is 0 only when every input is 0. Boolean expression: Q = A + B — read "Q equals A OR B". Here + means OR, not addition.

The OR gate

Q = 0

Output is 1 when at least one input is 1.

$Boolean expression: Q = A + B$

Try it:

Find the only row where the output is 0.

The NOT Gate

A NOT gate (also called an inverter) has one input . It outputs the opposite : 0 becomes 1 and 1 becomes 0. Boolean expression: Q = A — read "Q equals NOT A". The bar over the letter means NOT. You may also see A' or \negA . The small circle (the bubble) on the symbol always means NOT.

The NOT gate

Q = 1

A	Q
0	1
1	0

Output is the opposite of the input.

$Boolean expression: Q = A$

Try it:

Toggle A and watch the output flip.

The Three Basic Gates Together

Truth tables for AND, OR (two inputs) and NOT
Truth tables for AND, OR (two inputs) and NOT

Practice

For a 2-input OR gate, in how many of the 4 rows is the output 1?