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Tool 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 multiplicationab = a AND b and ! for logical NOT.

Literal notation

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.

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 (FND) uses a sum of products:

(a&&c)||b

The normal conjunctive form (FND) uses a product of sums:

(a||b)&&(b||c)

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Source code

dCode retains ownership of the source code of the script Boolean Expressions Calculator. 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, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the Boolean Expressions Calculator script for offline use, for you, your company or association, see you on contact page !

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