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
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.