Truth Table Generator

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus. It shows the functional values of logical expressions for every combination of values taken by their logical variables. Truth tables are widely used to check the validity of logical expressions, design digital circuits, and simplify boolean formulas.

This generator supports the following operators (case-insensitive):

• AND (&, &&, ∧) – conjunction, true only if both operands are true.
• OR (|, ||, ∨) – disjunction, true if at least one operand is true.
• NOT (~, !, ¬) – negation, unary operator that inverts the truth value.
• XOR (^, ⊕) – exclusive OR, true when operands differ.
• NAND – NOT AND (false only when both inputs are true).
• NOR – NOT OR (true only when both inputs are false).
• XNOR – exclusive NOR (true when operands are equal).
• IMP (->, →) – implication, equivalent to NOT A OR B.
• EQU (<->, ↔, <>, =) – equivalence, true when A and B have the same value.

Operators are evaluated in standard precedence order: NOT (highest) → AND, NAND, XOR → OR, NOR, XNOR → IMP → EQU (lowest). Use parentheses to override default precedence.

You can use up to 6 distinct single-letter variables (A–Z, case-insensitive, always treated as uppercase). With 6 variables the table contains 64 rows – still readable. For more variables, please simplify your expression or use propositional logic software. Multi‑letter variable names are not supported to keep the table clear.

Two logical expressions are equivalent if their truth tables are identical for every possible input combination. To check, generate the truth table for both expressions (e.g., A AND (B OR C) vs (A AND B) OR (A AND C)) and compare the output columns. This tool lets you quickly verify equivalences – just run each expression and compare the results side by side.

Truth tables are fundamental in digital electronics (logic gate design), computer science (circuit optimization, programming conditions), mathematics (propositional logic), and artificial intelligence (rule-based systems). Engineers use them to analyze and simplify combinational circuits, while students rely on truth tables to understand logical connectives and to prove identities in discrete math courses.

You can use double negation! NOT NOT A is perfectly valid and evaluates to A. Just type it exactly as shown – the tool will generate the correct truth table. Make sure to separate operators from variables with spaces or parentheses, e.g., NOT (NOT A) is also fine.