Conversion to DNF Disjunctive normal form

karnaugh map of disjunctive normal form (¬a∧¬b∧¬d) ∨ (¬a∧b∧c) ∨ (a∧b∧d) ∨ (a∧¬b∧¬c)



karnaugh map of disjunctive normal form (¬a∧c∧¬d) ∨ (b∧c∧d) ∨ (a∧¬c∧d) ∨ (¬b∧¬c∧¬d). despite different grouping, same fields contain 1 in previous map.

converting formula dnf involves using logical equivalences, such double negative elimination, de morgan s laws, , distributive law.

all logical formulas can converted equivalent disjunctive normal form. however, in cases conversion dnf can lead exponential explosion of formula. example, dnf of logical formula of following form has 2 terms:

(

x

1


∨

y

1


)
∧
(

x

2


∨

y

2


)
∧
⋯
∧
(

x

n


∨

y

n


)


{\displaystyle (x_{1}\lor y_{1})\land (x_{2}\lor y_{2})\land \dots \land (x_{n}\lor y_{n})}

any particular boolean function can represented 1 , 1 full disjunctive normal form, 1 of canonical forms. in contrast, 2 different plain disjunctive normal forms may denote same boolean function, see pictures.

cite error: there <ref group=note> tags on page, references not show without {{reflist|group=note}} template (see page).