Digital circuits represent logical states using physical signals. In an idealized binary model, two voltage ranges are interpreted as logical $0$ and $1$.

A logic gate implements a Boolean operation on those input states.

NOT, AND and OR

A NOT gate inverts one input. AND produces $1$ only when both inputs are $1$, while OR produces $1$ when at least one input is $1$.

Other useful gates such as NAND, NOR and XOR are built from related Boolean operations.

Physical signals are not perfect Booleans

Real voltages change continuously and require finite time to propagate through a circuit. Digital design works by defining ranges that count as logical states and by ensuring timing and noise remain within safe margins.

From algebra to circuits

A Boolean expression can be implemented by connecting gates whose output signals feed later inputs. The same Boolean function can often be represented by many different circuits.

Logic gates turn the abstract Boolean operations used in computation into physical building blocks for arithmetic, control and memory.