Truth Table Generator

This truth table generator builds the table for any propositional logic expression: type something like A AND (B OR NOT C) and the full table appears with every intermediate step. The tool also tells you whether the expression is a tautology, gives the DNF and CNF, and can compare two expressions.

Source: Wikipedia – Truth table (Aufbau, Zeilenzahl 2^n, Operatoren). Updated: 2 October 2026.

Logical expression

Variables are single letters (A–Z, up to 8). Operators: AND, OR, NOT, XOR, NAND, NOR, ->, <-> or ∧ ∨ ¬ ⊕ → ↔; parentheses are allowed

Second expression to compare (optional)

Checks whether both expressions agree for every input, e.g. for De Morgan’s laws

How to write the values

Put the “all true” row firstMany textbooks start this way; otherwise the “all false” row is on top

My ToolboxYour inputs are saved in this browser only.

Result

Classification: Satisfiable, but not a tautology – true in 3 of 8 rows
Read as: A ∧ (B ∨ ¬C)
Truth table: A B C ¬C B ∨ ¬C A ∧ (B ∨ ¬C)
0 0 0 1 1 0
0 0 1 0 0 0
0 1 0 1 1 0
0 1 1 0 1 0
1 0 0 1 1 1
1 0 1 0 0 0
1 1 0 1 1 1
1 1 1 0 1 1
Disjunctive normal form (DNF): (A ∧ ¬B ∧ ¬C) ∨ (A ∧ B ∧ ¬C) ∨ (A ∧ B ∧ C)
Conjunctive normal form (CNF): (A ∨ B ∨ C) ∧ (A ∨ B ∨ ¬C) ∧ (A ∨ ¬B ∨ C) ∧ (A ∨ ¬B ∨ ¬C) ∧ (¬A ∨ B ∨ ¬C)
Comparison: –

A	B	C	¬C	B ∨ ¬C	A ∧ (B ∨ ¬C)
0	0	0	1	1	0
0	0	1	0	0	0
0	1	0	1	1	0
0	1	1	0	1	0
1	0	0	1	1	1
1	0	1	0	0	0
1	1	0	1	1	1
1	1	1	0	1	1

How it is calculated

A truth table lists, for every combination of true and false values of the variables, the value a logical expression takes. With n variables it has 2 to the power n rows: two variables give 4, three give 8, eight give 256 rows. The generator adds a column for each sub-expression so you can follow the evaluation step by step.

How to enter expressions

AND (∧): AND, & or ∧. OR (∨): OR, | or ∨. The caret ^ is read as AND.
NOT (¬): NOT, ! or ¬. XOR (⊕): XOR or ⊕. NAND and NOR work too.
Implication (→): -> or →. Equivalence (↔): <-> or ↔.
Precedence: NOT binds tightest, then AND, XOR, OR, → and finally ↔. The arrow → is read right to left. When in doubt, add parentheses; the “Read as” line shows how the expression was understood.

Tautology, contradiction and normal forms

If the last column is true in every row, the expression is a tautology (such as A ∨ ¬A); if it is false everywhere, it is a contradiction (A ∧ ¬A). Anything in between is satisfiable. The disjunctive normal form (DNF) joins the true rows with OR; the conjunctive normal form (CNF) negates the false rows and joins them with AND. The second input field lets you check laws such as De Morgan’s: ¬(A ∧ B) and ¬A ∨ ¬B are equivalent. To convert numbers between systems, use the number base converter, and for bitwise logic on binary numbers the binary calculator.

Frequently asked questions

How do I make a truth table?

Assign every combination of true and false to the variables (2 to the power n rows), then evaluate the expression from the inside out, one sub-expression per column. The generator does this automatically and shows all steps.

What are the truth tables for AND, OR and XOR?

AND is true only if both inputs are true. OR is true if at least one is true. XOR is true if exactly one is true. Enter A AND B, A OR B or A XOR B to see each table.

What is a tautology?

An expression that is true for every input, such as A ∨ ¬A. Its counterpart, the contradiction, is always false, for example A ∧ ¬A.

What are DNF and CNF?

Normal forms of an expression. The DNF is an OR of AND terms (one per true row), the CNF an AND of OR terms (one per false row). Both can be read straight from the table.

How can I check whether two expressions are equivalent?

Enter both. The tool compares them in every row and gives a counterexample if they differ. Equivalent means that both have the same value in every row.

Sources and legal basis

As of: 2 October 2026 · Editorial policy