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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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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