Tool/Calculator to simplify or minify Boolean expressions (Boolean algebra) containing logical expressions with AND, OR, NOT, XOR.
Boolean Expressions Calculator - dCode
Tag(s) : Symbolic Computation, Electronics
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Boolean Expressions Calculator
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Boolean Expressions Simplificator
Tool/Calculator to simplify or minify Boolean expressions (Boolean algebra) containing logical expressions with AND, OR, NOT, XOR.
Answers to Questions
How to simplify / minify a boolean expression?
The simplification of Boolean Equations can use different methods: besides the classical development via associativity, commutativity, distributivity, etc., Truth tables or Venn diagrams provide a good overview of the expressions.
dCode allows several syntaxes:
Algebraic notation
!(ab(c+!d))+!b with implicit multiplication ab = a AND b and ! for logical NOT.
Literal notation
Example: NOT (a AND b AND (c OR NOT d)) OR NOT b
There may be several minimal representations for the same expression, dCode provides a solution and output an algebraic notation.
Functional notation XOR(a,b) are not taken into account, please write a XOR b
How to show/demonstrate that 2 boolean expression are equal?
Method 1: simplify them until you get the same writing.
Method 2: by calculating their truth table which should be identical.
What is De Morgan's law?
De Morgan's laws are often used to rewrite logical expressions. They are generally stated: not (A and B) = (not A) or (not B) and not (A or B) = (not A) and (not B). Here are the equivalent logical entries:
$$ \overline{(A \land B)} \leftrightarrow (\overline{A})\lor (\overline{B}) \iff \bar{AB} = \bar{A} + \bar{B} $$
$$ \overline{(A \lor B)} \leftrightarrow (\overline{A}) \land (\overline{B}) \iff \bar{A+B} = \bar{A} . \bar{B} $$
What is Disjunctive or Conjuctive Normal Form?
In logic, it is possible to use different formats to ensure better readability or usability.
The normal disjunctive form (DNF) uses a sum of products:
Example: (a&&c)||b
The normal conjunctive form (CNF) or clausal form uses a product of sums:
Example: (a||b)&&(b||c)
How to show step by step calculation?
The calculation steps such as a human imagine them do not exist for the solver. The operations performed are binary bit-by-bit and do not correspond to those performed during a resolution with a pencil and a paper.
Source code
dCode retains ownership of the source code of the script Boolean Expressions Calculator online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Boolean Expressions Calculator script for offline use on PC, iPhone or Android, ask for price quote on contact page !
Questions / Comments
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