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Boolean Expressions

Boolean Expressions: Two Variables


Input




Expression

Boolean Expression

Logical Notation



Q =

Binary Output

0 0 0 0

True/False Output

false false false false

Truth Table Output Values

A B Q
0 0 0
0 1 0
1 0 0
1 1 0

Q =

Truth Table with Calculations

A B Q
0 0 0
0 1 0
1 0 0
1 1 0


Q =

Simplifying the Boolean Expression

 Expression
Reason

 

Truth Table for Simplified Expression

A B Q
0 0 0
0 1 0
1 0 0
1 1 0

Q =

Simplified Logical Expression:

Karnaugh Map



Input




Expression

Boolean Expression

Logical Notation



Q =

Binary Output

0 0 0 0 0 0 0 0

True/False Output

false false false false false false false false

Truth Table Output Values

A B C Q
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 0

Q =

Truth Table with Calculations

A B C Q
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 0


Q =

Simplifying the Boolean Expression

 Expression
Reason

 

Truth Table for Simplified Expression

A B C Q
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 0

Q =

Simplified Logical Expression:

Karnaugh Map



Input




Expression

Boolean Expression

Logical Notation



Q =

Binary Output

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

True/False Output

false false false false false false false false false false false false false false false false

Truth Table Output Values

A B C D Q
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
0 0 1 1 0
0 1 0 0 0
0 1 0 1 0
0 1 1 0 0
0 1 1 1 0
1 0 0 0 0
1 0 0 1 0
1 0 1 0 0
1 0 1 1 0
1 1 0 0 0
1 1 0 1 0
1 1 1 0 0
1 1 1 1 0

Q =

Truth Table with Calculations

A B C D Q
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
0 0 1 1 0
0 1 0 0 0
0 1 0 1 0
0 1 1 0 0
0 1 1 1 0
1 0 0 0 0
1 0 0 1 0
1 0 1 0 0
1 0 1 1 0
1 1 0 0 0
1 1 0 1 0
1 1 1 0 0
1 1 1 1 0


Q =

Simplifying the Boolean Expression

 Expression
Reason

 

Truth Table for Simplified Expression

A B C D Q
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
0 0 1 1 0
0 1 0 0 0
0 1 0 1 0
0 1 1 0 0
0 1 1 1 0
1 0 0 0 0
1 0 0 1 0
1 0 1 0 0
1 0 1 1 0
1 1 0 0 0
1 1 0 1 0
1 1 1 0 0
1 1 1 1 0

Q =

Simplified Logical Expression:

Karnaugh Map


About the Tool

This tool can be used to enter Boolean expressions using two, three or four variables and the following logical operations

  • NOT
  • AND
  • OR
  • XOR
  • NAND
  • NOR

Brackets can also be used


The tool then generates the following

  • The expression formatted as a Boolean expression using · for AND, + for OR, ⊕ for XOR and ~ for NOT
  • The expression formatted in logical notation using ∧ for AND, ∨ for OR, ⊻ for XOR and ¬ for NOT
  • The output for the different combinations of inputs to the Boolean variables using 1 and 0
  • The output for the different combinations of inputs to the Boolean variables using true and false
  • A truth table with the resulting output
  • A truth table showing the step bu step calculations used to derive the output
  • The process of simplifying the expression down to a series of just ANDs and ORs
  • A truth table showing the step bu step calculations used to derive the output from the simplified expression
  • A Karnaugh Map for the simplified expression

Contents Copyright 2026 Andy Abraham

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