Full conjunctions can be numbered naturally. Think of the variables in a row, e.g. B. . If the respective literal occurs negated for a concrete full conjunction , it is replaced by a 0, otherwise by a 1. A binary number is created that can be interpreted in decimal form. This decimal number is known as the number or index of the minterm. If you want to designate this minterm via its index , you write . The same goes for the maxterms for disjunctions.
Comparison of Minterm / Maxterm
The following table shows the difference between the Maxterm and Minterm representation:
index
Minterm
Max term
0
0
0
0
1
0
0
1
2
0
1
0
3
0
1
1
4th
1
0
0
5
1
0
1
6th
1
1
0
7th
1
1
1
Realization of decoder circuits with minter terms / max terms:
Minterm
Max term
0
NOR gate
AND gate
1
OR gate
NAND gate
Designations
Minterme
A single minterm:
For exactly one assignment of function value 1
Minimality:
maximum number of zeros
minimum number of ones
(apart from the trivial null function)
Maxterms
A single maxterm:
Function value 0 for exactly one assignment
Maximality:
maximum number of ones
minimum number of zeros
(apart from the trivial one function)
Relation to the Karnaugh-Veitch diagram
One also speaks of the minterm of a function if this implies , i. H. if applies
.
Here is the vector of the input variable. Such minterms , in a reversible manner, unambiguously correspond to those fields of a Karnaugh-Veitch diagram which contain the value 1 for the function under consideration.