Boolean function

Definition

Let $n$ be a natural number. A Boolean function of $n$ variables is a function $f : \{0, 1\}^n \to \{0, 1\}$.

Remarks

There are $2^n$ inputs, so there are $2^{2^n}$ Boolean functions of $n$ variables. A truth table lists the values of a Boolean function on all inputs. Every Boolean function is given by a formula in disjunctive normal form, and also by one in conjunctive normal form.

Explanations

L1 human

A Boolean function takes some bits as input and returns one bit. The logic gates and, or and not are Boolean functions, and a digital circuit computes a Boolean function.