# 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 .