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Truth Table Generator

Generate truth tables for Boolean logic expressions with AND, OR, NOT, XOR, NAND, NOR, and implication operators with step-by-step evaluation.

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What Is a Truth Table?

A truth table shows how the truth value of a compound logical expression depends on its input variables. Each row represents one combination of true/false inputs and the resulting output.

See also: NAND Binary Calculator and Karnaugh Map Solver.

How to Build a Truth Table

  1. List all input variables (A, B, C, ...).
  2. Create columns for each variable plus the result.
  3. Fill rows with all $2^n$ combinations of T and F.
  4. Evaluate the expression for each row.

Logic Gate Truth Tables

AND: true only when both inputs are true.

OR: true when at least one input is true.

XOR: true when exactly one input is true.

NOT: flips the input value.

Supported Operators

NOT, AND, OR, XOR, NAND, NOR, XNOR, and IMPLIES (written as -> or ).

Frequently Asked Questions

How many rows does a truth table have?

For n variables, a complete truth table has 2^n rows. This calculator supports up to 6 variables (64 rows).

What is a tautology?

A tautology is a logical expression that is always true regardless of input values. Every row in its truth table shows T.

What are universal logic gates?

NAND and NOR are universal gates. Any other logic gate can be built using only NAND or only NOR gates.

How do I write an implication in the expression?

Use A -> B or A → B. Implication is false only when A is true and B is false.