mintermen

Minterm, in Boolean algebra and digital logic, refers to a product term that represents a single combination of input variables. The plural is minterms in English, though in some languages the form mintermen is used. A minterm is a conjunction of all input variables, where each variable appears either complemented or uncomplemented.

Formally, for n variables x1, x2, ..., xn, a minterm Mi is the product xi or ¬xi for every i, chosen so that Mi is true for exactly one input vector and false for all others. The set of all 2^n minterms corresponds to the rows of the truth table for the variables. Each minterm has a unique index i, often aligned with the binary pattern of the variables. In canonical notation, a Boolean function f(x1,...,xn) can be written as a sum (OR) of the minterms for which f equals 1: f = ∑ Mi.

Minterms are contrasted with maxterms, which are sum terms that are false for exactly one input vector and true for all others. Canonical forms such as the sum of minterms (SOP) and the product of maxterms (POS) express functions in standard, complete forms. Minterms are commonly used in Karnaugh maps and Boolean algebra to simplify expressions and analyze digital circuits.

Example: for two variables x and y, the four minterms are M0 = ¬x ∧ ¬y, M1 = ¬x ∧ y, M2 = x ∧ ¬y, M3 = x ∧ y. A function f = x ∨ y can be written as f = M1 ∨ M2 ∨ M3.