Boolean Algebra Calculator

Simplify Boolean expressions and generate truth tables. Supports AND (&), OR (|), NOT (~), NAND, NOR, XOR (^), XNOR operations.

Operators: & (AND), | (OR), ~ (NOT), ^ (XOR)
Variables: A, B, C, D (single letters)
Simplified Expression
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Truth Table

Step-by-Step Solution

Enter a Boolean expression and click "Calculate" to see the step-by-step simplification.

Boolean Operators

  • AND (&): True only if both inputs are true
  • OR (|): True if at least one input is true
  • NOT (~): Inverts the input
  • XOR (^): True if inputs are different
  • NAND: NOT AND
  • NOR: NOT OR

Boolean Laws

  • Identity: A & 1 = A, A | 0 = A
  • Null: A & 0 = 0, A | 1 = 1
  • Idempotent: A & A = A, A | A = A
  • Complement: A & ~A = 0, A | ~A = 1
  • De Morgan's: ~(A & B) = ~A | ~B
  • De Morgan's: ~(A | B) = ~A & ~B

Example Expressions

  • A & B = A AND B
  • A | B = A OR B
  • ~A & B = NOT A AND B
  • (A & B) | (~A & C) = If-Then-Else
  • A ^ B = A XOR B