Editing Canonical normal form (section)

{{Short description|Standard forms of Boolean functions}}
{{about-distinguish|canonical forms particularly in Boolean algebra|Canonical form|Normal form (disambiguation){{!}}Normal form}}
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* This article '''presents an incomplete view of the subject'''.
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{{anchor|SOP|POS}}In [[Boolean algebra (logic)|Boolean algebra]], any [[Boolean function]] can be expressed in the '''canonical disjunctive normal form''' ('''[[Disjunctive normal form|CDNF]]'''),<ref name="PahlDamrath2012">{{cite book|author1=Peter J. Pahl|author2=Rudolf Damrath|title=Mathematical Foundations of Computational Engineering: A Handbook|url=https://books.google.com/books?id=FRfrCAAAQBAJ&q=%22Canonical+disjunctive+normal+form%22&pg=PA15|date=6 December 2012|publisher=Springer Science & Business Media|isbn=978-3-642-56893-0|pages=15–}}</ref> '''minterm canonical form''', or '''Sum of Products''' ('''SoP''' or '''SOP''') as a disjunction (OR) of minterms. The [[De Morgan dual]] is the '''canonical conjunctive normal form''' ('''[[Conjunctive normal form|CCNF]]'''), '''maxterm canonical form''', or '''Product of Sums''' ('''PoS''' or '''POS''') which is a conjunction (AND) of maxterms. These forms can be useful for the simplification of Boolean functions, which is of great importance in the optimization of Boolean formulas in general and [[digital circuit]]s in particular.

Other [[canonical form]]s 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).