Generate a Boolean truth table

Evaluate every true-and-false assignment for a Boolean expression containing AND, OR, XOR, NOT, and parentheses.

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ToolTruth Table Generator
Input
Output
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Preview

How it works

A tokenizer recognizes variable names, parentheses, word operators, and the aliases &, |, ^, and !; recursive-descent parsing applies NOT before AND, AND before XOR, and XOR before OR. The parsed expression is evaluated for all 2ⁿ assignments from the all-true row to the all-false row.

Formula
row count = 2ⁿ for n distinct variables
  • No expression is assumed, and six variables cap the visible output at 64 rows.
  • Variable order follows first appearance in the expression.

Worked example

Two variables with AND
Input
											p AND q
Output
												Table: p q | Result
T T | T
T F | F
F T | F
F F | F
Variable count: 2
Row count: 4
True count: 1
False count: 3

When to use this

Propositional-logic exercises classify assignments, digital-logic design checks gate combinations, and software reviews compare condition columns for logical equivalence.

Edge cases

  • p OR q AND r means p OR (q AND r) because AND binds more tightly; add parentheses to request (p OR q) AND r.
  • p XOR q XOR r parses from the left, while Boolean XOR’s associativity means the final parity column is unchanged.
  • Seven distinct variables would produce 128 rows and are rejected by the six-variable readability cap.