This article is about canonical forms particularly in Boolean algebra. It is not to be confused with Canonical form or Normal form.
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In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form (CDNF)[1] or minterm canonical form, and its dual, the canonical conjunctive normal form (CCNF) or maxterm canonical form. Other canonical forms include the complete sum of prime implicants or Blake canonical form (and its dual), and the algebraic normal form (also called Zhegalkin or Reed–Muller).
Minterms are called products because they are the logical AND of a set of variables, and maxterms are called sums because they are the logical OR of a set of variables. These concepts are dual because of their complementary-symmetry relationship as expressed by De Morgan's laws.
Two dual canonical forms of any Boolean function are a "sum of minterms" and a "product of maxterms." The term "Sum of Products" (SoP or SOP) is widely used for the canonical form that is a disjunction (OR) of minterms. Its De Morgan dual is a "Product of Sums" (PoS or POS) for the canonical form that is a conjunction (AND) of maxterms. These forms can be useful for the simplification of these functions, which is of great importance in the optimization of Boolean formulas in general and digital circuits in particular.
^Peter J. Pahl; Rudolf Damrath (2012-12-06). Mathematical Foundations of Computational Engineering: A Handbook. Springer Science & Business Media. pp. 15–. ISBN 978-3-642-56893-0.
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