Search for a tool
Boolean Expressions Calculator

Tool/Calculator to simplify or minify Boolean expressions (Boolean algebra) containing logical expressions with AND, OR, NOT, XOR.

Results

Boolean Expressions Calculator -

Tag(s) : Symbolic Computation, Electronics

dCode and you

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!
You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? Contact-me!

Team dCode likes feedback and relevant comments; to get an answer give an email (not published). It is thanks to you that dCode has the best Boolean Expressions Calculator tool. Thank you.

# Boolean Expressions Calculator

## Boolean Expressions Simplificator

 Format Automatic Logical Format Disjunctive Normal Form DNF (Sum of products) Conjunctive Normal Form CNF (Product of Sums)
 Notation Algebraic (&&, ||, !) Litteral (AND, OR, NOT)

Tool/Calculator to simplify or minify Boolean expressions (Boolean algebra) containing logical expressions with AND, OR, NOT, XOR.

### 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.

### 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) 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 given 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 !