Boolean function

In mathematics, a Boolean function usually means a function

F(b₁, b₂, ... , b_n)

of a number n of Boolean variables b_i from the two-element Boolean algebra {0,1}, and such that F also takes values in {0,1}. A function on a general function domain taking values in {0,1} would be called a Boolean-valued function, so that Boolean functions are a special case.

There are 2ⁿ such functions; these play a basic role in questions of complexity theory as well as the design of circuits and chips for digital computers.