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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Boolean Minterms and Maxterms
Maxterms/Minterms Calculator
Answers to Questions (FAQ)
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. The minterm is described as a sum of products (SOP).
Example: a OR b OR !c = 1 or (a AND NOT(b)) OR (NOT(c) AND d) = 1 are minterms
Each row of a logical truth table with value 1/True can therefore be associated to exactly one minterm.
A Boolean expression expressed as a sum of products (SOP) is also described as a disjunctive normal form (DNF).
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. The maxterm is described as a sum of product (SOP).
Example: a AND b AND c = 0 or (NOT(a) OR b) AND (NOT(c) OR d) = 0 are maxterms
Each row of a logical truth table worth 0/False can therefore be associated to exactly one maxterm.
A Boolean expression expressed as a product of sums (POS) is also described as conjunctive normal form (CNF).
How to calculate minterms and maxterms from the truth table?
The minterms are the Boolean expressions corresponding to the true/1 rows and the maxterms are those of the false/0 rows.
Example: The function F has for logical truth table
| a | b | F |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
On dCode, 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 simplified canonical form minterm/maxterm a (identical in this case)
How to calculate a minterm from a truth table?
The minterms of a boolean function are the aggregates of each row true of the truth table linked with logical OR.
Example: The minterms are the rows with value 1 being the rows 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
How to calculate a maxterm from a truth table?
The maxterms of a function are the aggregates of each maxterm of the logical array with logical ANDs.
The maxterms are the rows with value 0 being the rows 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.
What is the difference between minterm and maxterm?
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 are maxterms
Each row of a logical truth table worth 0/False can therefore be associated to exactly one maxterm.
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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- Maxterms/Minterms Calculator
- What is a Boolean minterm? (Definition)
- What is a Boolean maxterm? (Definition)
- How to calculate minterms and maxterms from the truth table?
- How to calculate a minterm from a truth table?
- How to calculate a maxterm from a truth table?
- What is the difference between minterm and maxterm?
