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Boolean Expressions Calculator

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

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Boolean Expressions Calculator -

Tag(s) : Mathematics, Electronics

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# Boolean Expressions Calculator

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## Boolean Expressions Simplificator

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

Tool 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 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:

Example: (a&&c)||b

The normal conjunctive form (FND) 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.