DNF and CNF

Conjunctive normal form CNF and Disjunctive normal form DNF

The disjunctive normal form and the conjunctive normal form are a standard way to express the function of a logic control in boolean form.  They are usually derived from the truth table.

Disjunctive und Conjunctive Normal Form

Disjunctive normal form (DNF)

1. Marking the lines whose output variable has the status logic "1".
2. The input variables of a line are linked with logic "and". Within a line, the input variables with the status "0" are negated. Such a term is referred to as a "minterm".
3. All minterms are now OR-linked

Conjunctive normal form (CNF)

1. Select the lines whose output variable has the status logic "0".
2. The input variables of a line are linked with logic "or". Within a line, the input variables with the status "1" are negated. Such a term is referred to as a "maxterm".
3. All maxterms are now combined with logic "and".

Application example:

A system has two control points for switching on. The system should only start if only one button is pressed at a time. As soon as both inputs are pressed simultaneously, the system remains in stop.

Two different equations can be created using the truth table: the disjunctive normal form and the conjunctive normal form, as described above.

Disjunctive normal form (DNF) and Conjunctive normal form (CNF) example

How to convert the Disjunctive Normal Form to Conjunctive Normal Form

Both the DNF and the CNF describe the same truth table. Accordingly, it should be possible to convert the DNF into the KNF and vice versa using Boolean algebra. We show the conversion DNF to CNF:

Convert Disjunctive to Conjunctive Normal Form