Editing Boolean function (section)

== Representation ==
[[File:Three input boolean circuit.svg|thumb|A Boolean function represented as a [[Boolean circuit]]]]
A Boolean function may be specified in a variety of ways:

* [[Truth table]]: explicitly listing its value for all possible values of the arguments
**Marquand diagram: truth table values arranged in a two-dimensional grid (used in a [[Karnaugh map]])
**[[Binary decision diagram]], listing the truth table values at the bottom of a binary tree
**[[Venn diagram]], depicting the truth table values as a colouring of regions of the plane
Algebraically, as a [[propositional formula]] using rudimentary Boolean functions:

* [[Negation normal form]], an arbitrary mix of AND and ORs of the arguments and their complements
* [[Disjunctive normal form]], as an OR of ANDs of the arguments and their complements
* [[Conjunctive normal form]], as an AND of ORs of the arguments and their complements
*[[Canonical normal form]], a standardized formula which uniquely identifies the function:
**[[Algebraic normal form]] or [[Zhegalkin polynomial]], as a XOR of ANDs of the arguments (no complements allowed)
**''Full'' (canonical) [[disjunctive normal form]], an OR of ANDs each containing every argument or complement ([[minterms]])
**''Full'' (canonical) [[conjunctive normal form]], an AND of ORs each containing every argument or complement ([[maxterms]])
**[[Blake canonical form]], the OR of all the [[prime implicant]]s of the function
Boolean formulas can also be displayed as a graph:
* [[Propositional directed acyclic graph]]
**[[Circuit (computer science)|Digital circuit]] diagram of [[logic gate]]s, a [[Boolean circuit]]
**[[And-inverter graph]], using only AND and NOT
In order to optimize electronic circuits, Boolean formulas can be [[Minimization of Boolean functions|minimized]] using the [[Quine–McCluskey algorithm]] or [[Karnaugh map]].