Boolean Algebra Simplifier

Simplify Logic Expressions

Simplify boolean algebra expressions using laws and theorems with step-by-step solutions.

Boolean Expression

Use: A-Z (variables), · (AND), + (OR), ! (NOT), () (parentheses)

Notation Guide

· = AND operation (multiplication)

+ = OR operation (addition)

! = NOT operation (negation)

Variables: Use uppercase letters (A, B, C, etc.)

Boolean Laws

Identity:

A+0=A, A·1=A

Null:

A+1=1, A·0=0

Idempotent:

A+A=A, A·A=A

Complement:

A+!A=1, A·!A=0

De Morgan's:

!(A+B)=!A·!B

!(A·B)=!A+!B

Absorption:

A+A·B=A

A·(A+B)=A

Features

  • Step-by-step simplification
  • Truth table generation
  • Multiple boolean laws applied
  • Variable extraction
  • Expression evaluation
  • Quick examples
  • Copy simplified result

Applications

  • Digital circuit design
  • Logic gate optimization
  • Computer architecture
  • Programming logic
  • Database query optimization
  • Artificial intelligence
  • Control systems
  • Hardware description languages

Tips

Simplification Benefits:

  • Reduces circuit complexity
  • Minimizes gate count
  • Improves performance
  • Reduces power consumption
  • Easier to understand logic