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

Boolean Minterms and Maxterms - dCode

Tag(s) : Symbolic Computation, Electronics

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

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**.

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**.

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

a | b | F |
---|---|---|

0 | 0 | 0 |

0 | 1 | 0 |

1 | 0 | 1 |

1 | 1 | 1 |

__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.

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