Boolean Algebra Calculator - Free Online Simplifier

Advanced boolean algebra calculator that simplifies expressions instantly. Get step-by-step solutions, truth tables, K-maps, and logic diagrams for any Boolean expression.

How to Use the Calculator

  1. 1. Enter Expression: Type your Boolean expression using variables A, B, C, D, E
  2. 2. Use Operators: AND (&), OR (|), NOT (!), XOR (^), parentheses for grouping
  3. 3. Calculate: Click calculate to generate truth table and simplification
  4. 4. View Results: See step-by-step simplification and K-map visualization
  5. 5. Export: Download results as PDF or CSV for your projects

Supported Operations

AND: A & B, A * B, AB
OR: A | B, A + B
NOT: !A, ~A, A'
XOR: A ^ B, A ⊕ B
NAND: !(A & B)
NOR: !(A | B)
Grouping: Use parentheses ( )

Boolean Algebra Simplification Rules

Basic 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

Advanced Laws

  • • Absorption: A + AB = A, A(A + B) = A
  • • De Morgan's: (A + B)' = A' · B'
  • • Distributive: A(B + C) = AB + AC
  • • Consensus: AB + A'C + BC = AB + A'C

Example Expressions

  • A & B | C
  • !(A | B) & C
  • A ^ B ^ C
  • (A | B) & (!A | C)

Features

  • • Up to 5 variables (A-E)
  • • Step-by-step simplification
  • • Truth table generation
  • • K-map visualization
  • • PDF/CSV export

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