Truth Table Generator

Instantly solve complex logical problems with our free online Logic Calculator.

Your Premier Boolean Expression Solver

The Truth Table Generator is an essential digital logic tool for students, engineers, and computer scientists. Easily input any propositional logic solver expression—from simple conjunctions (A∧B) to complex biconditionals ((A→B)↔C)—and our system will instantly produce a complete, detailed truth table. This is the fastest way to confirm whether your boolean algebra calculator results in a tautology, contradiction, or contingency. Stop guessing at solutions and start learning the fundamental principles of logic expression evaluation with speed and accuracy. Use the list of accepted symbols below, enter your expressions, and hit 'Generate' to begin.

Enter Logic Expressions

Variables detected: 0 (2^0 rows)

Syntax & Operators Help

Negation (NOT): ¬, !, ~

Conjunction (AND): ∧, &, &&

Disjunction (OR): ∨, |, ||

Exclusive OR (XOR): ⇹, !=, ,

Conditional (Implies): →, >, ->, =>

Biconditional (IFF): ↔, =, ==, <>, <=>, <->

NAND/NOR: Not implemented as separate tokens, use parentheses: e.g., ¬(A∧B) or ¬(A∨B)

Variables: Single letters (A-Z, case-insensitive).

Frequently Asked Questions (FAQ)

What is a truth table and why is it important?
A truth table is a mathematical table used in logic to determine the functional values of propositional expressions on each combination of truth values (True or False) for the input variables. They are crucial for designing digital circuits, validating complex logic, and simplifying boolean algebra expressions.
How do I use this online truth table generator?
Simply type your logical expression into the input box. You can use standard symbols like ∧ (AND), ∨ (OR), ¬ (NOT), → (Implies), or their ASCII equivalents (&, |, !, ->). Separate multiple expressions with a comma. The calculator handles the rest, generating the full table and evaluating whether the result is a tautology, contradiction, or contingency.
What symbols are accepted by the logic calculator?
The calculator accepts both standard logic symbols and common ASCII alternatives. For NOT: ¬, !, ~. For AND: ∧, &, &&. For OR: ∨, |, ||. For Implies: →, >, ->. For IFF: ↔, =, <->. Parentheses () are also fully supported for grouping.
Can this tool be used as a digital logic tool?
Yes, truth tables are the foundation of digital logic design. The results directly map to the output of logic gates (AND, OR, NOT, XOR), making this generator perfect for verifying circuits before building them, simplifying expressions (logic simplifier), and understanding gate operation.