Product term

In Boolean logic, a product term is a conjunction of literals, where each literal is either a variable or its negation.

Examples

Examples of product terms include:

[math]\displaystyle{ A \wedge B }[/math]

[math]\displaystyle{ A \wedge (\neg B) \wedge (\neg C) }[/math]

[math]\displaystyle{ \neg A }[/math]

Origin

The terminology comes from the similarity of AND to multiplication as in the ring structure of Boolean rings.

Minterms

For a boolean function of [math]\displaystyle{ n }[/math] variables [math]\displaystyle{ {x_1,\dots,x_n} }[/math], a product term in which each of the [math]\displaystyle{ n }[/math] variables appears once (in either its complemented or uncomplemented form) is called a minterm. Thus, a minterm is a logical expression of n variables that employs only the complement operator and the conjunction operator.

References

• Fredrick J. Hill, and Gerald R. Peterson, 1974, Introduction to Switching Theory and Logical Design, Second Edition, John Wiley & Sons, NY, ISBN 0-471-39882-9