# Full disjunction

A full disjunction (also: max term ) is a special disjunction term in propositional logic . H. a number of literals , all linked by a logical or ( ). All variables of the considered -digit Boolean function must appear in the disjunction term in order to be able to speak of a full disjunction. Examples are: ${\ displaystyle \ vee}$ ${\ displaystyle n}$ ${\ displaystyle n}$ • ${\ displaystyle e_ {1} \ vee e_ {2}}$ • ${\ displaystyle e_ {1} \ vee \ neg e_ {2} \ vee e_ {3}}$ • ${\ displaystyle \ neg e_ {1} \ vee e_ {2} \ vee e_ {3}}$ Full disjunctions can be combined to form a conjunctive normal form.

## Comparison of Minterm / Maxterm

The following table shows the difference between the maxterm and minterm representation :

index ${\ displaystyle x_ {2}}$ ${\ displaystyle x_ {1}}$ ${\ displaystyle x_ {0}}$ Minterm Max term
0 0 0 0 ${\ displaystyle \ neg x_ {2} \ wedge \ neg x_ {1} \ wedge \ neg x_ {0}}$ ${\ displaystyle x_ {2} \ vee x_ ​​{1} \ vee x_ ​​{0}}$ 1 0 0 1 ${\ displaystyle \ neg x_ {2} \ wedge \ neg x_ {1} \ wedge x_ {0}}$ ${\ displaystyle x_ {2} \ vee x_ ​​{1} \ vee \ neg x_ {0}}$ 2 0 1 0 ${\ displaystyle \ neg x_ {2} \ wedge x_ {1} \ wedge \ neg x_ {0}}$ ${\ displaystyle x_ {2} \ vee \ neg x_ {1} \ vee x_ ​​{0}}$ 3 0 1 1 ${\ displaystyle \ neg x_ {2} \ wedge x_ {1} \ wedge x_ {0}}$ ${\ displaystyle x_ {2} \ vee \ neg x_ {1} \ vee \ neg x_ {0}}$ 4th 1 0 0 ${\ displaystyle x_ {2} \ wedge \ neg x_ {1} \ wedge \ neg x_ {0}}$ ${\ displaystyle \ neg x_ {2} \ vee x_ ​​{1} \ vee x_ ​​{0}}$ 5 1 0 1 ${\ displaystyle x_ {2} \ wedge \ neg x_ {1} \ wedge x_ {0}}$ ${\ displaystyle \ neg x_ {2} \ vee x_ ​​{1} \ vee \ neg x_ {0}}$ 6th 1 1 0 ${\ displaystyle x_ {2} \ wedge x_ {1} \ wedge \ neg x_ {0}}$ ${\ displaystyle \ neg x_ {2} \ vee \ neg x_ {1} \ vee x_ ​​{0}}$ 7th 1 1 1 ${\ displaystyle x_ {2} \ wedge x_ {1} \ wedge x_ {0}}$ ${\ displaystyle \ neg x_ {2} \ vee \ neg x_ {1} \ vee \ neg x_ {0}}$ Realization of circuits with mintermen / maxterms:

Minterm Max term
0 NOR gate AND gate
1 OR gate NAND gate

There are also full conjunctions .