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Boolean Minterms and Maxterms

Tool for calculating Minterms (canonical disjunctive normal form) and Maxterms (canonical conjunctive normal form) from a truth table of a unknown Boolean expression.

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Boolean Minterms and Maxterms -

Tag(s) : Symbolic Computation, Electronics

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# Boolean Minterms and Maxterms

## Maxterms/Minterms Calculator

 Notation désirée Algebraic (*, +, !) Logical (∧, ∨, ¬) Programming (&&, ||, ~) Literal (AND, OR, NOT)

### From the Truth Table

 Boolean Table From 0,...,0 to 1,...,1 From 1,...,1 to 0,...,0

### What is a Boolean minterm? (Definition)

A minterm is an expression regrouping the Boolean variables, complemented or not (a or not (a)), linked by logical ANDs and with a value of 1.

Example: a AND b AND c = 1 or NOT(a) AND b AND NOT(c) AND d = 1

Each line of a logical truth table with value 1/True can therefore be associated to exactly one minterm.

### What is a Boolean maxterm? (Definition)

A maxterm is an expression grouping Boolean variables, complemented or not (a or not (a)), linked by logical ORs and with a value of 0.

Example: a OR b OR c = 0 or a OR NOT(b) OR NOT(c) OR d = 0

Each line of a logical truth table worth 0/False can therefore be associated o exactly one maxterm.

### How to calculate a minterm or a maxterm from a truth table?

The minterms of a boolean function are the aggregates of each minterm of the logical array with logical OR.

The maxterms of a function are the aggregates of each maxterm of the logical array with logical ANDs.

Example: The function F has truth table

abF
000
010
101
111

Example: The minterms are the lines with value 1 being the lines 3 (a*!b=1) and 4 (a*b=1) so the minterms of F are the function (a*!b)+(a*b) which after boolean simplification gives a
The maxterms are the lines with value 0 being the lines 1 (a+b=0) and 2 (a+!b=0) thus the maxterms of F are the function (a+b)*(a+!b) which after boolean simplification is worth a.

Indicate the Boolean output values of the logical expression, ie. the sequence of 0 and 1 representing the last column of the Boolean truth table. dCode will compute compatible sets of variables and simplify the result.

Example: Enter 0011 (from 00 to 11) as the output values of the F Truth Table to obtain for minterm a and maxterm a

The minterms and maxterms are two ways to see the same logical Boolean expression either with its 0 or with its 1 logic.

## Source code

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