What operators does this truth table generator support?

This generator supports AND (&&, &, ∧), OR (||, |, ∨), NOT (!, ~, ¬), XOR (^, ⊕), NAND, NOR, XNOR (⊙), IMPLIES (→, =>), and BICONDITIONAL (↔, ). You can use parentheses for grouping.

How many variables can I use in a truth table?

This tool supports up to 8 variables (A through H). The number of rows doubles with each variable: 2 variables produce 4 rows, 3 variables produce 8 rows, and 8 variables produce 256 rows.

What is the difference between XOR and XNOR?

XOR (exclusive OR) returns true when exactly one of the inputs is true. XNOR (exclusive NOR) is the negation of XOR — it returns true when both inputs are the same (both true or both false). XNOR is also called the biconditional or equivalence operator.

Truth Table Generator

Q: What is a truth table?

A truth table is a mathematical table used to determine whether a compound boolean expression is true or false for every possible combination of input values. Each row represents a unique combination of variable values, and the final column shows the result of the expression.

Generate truth tables for any boolean logic expression. Supports AND, OR, NOT, XOR, NAND, NOR, XNOR, and conditional operators. Visualize logic gates with animated evaluation.

Free to useNo sign-up requiredUpdated Feb 2026

Truth Table GeneratorTry it now — free ▼

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Configure Expression

Enter a boolean logic expression with variables A-H

⚡ Quick Examples

Boolean Expression

Use uppercase letters A-H as variables. Supports AND, OR, NOT, XOR, NAND, NOR, XNOR, IMPLIES (→), IFF (↔).

Show Sub-expressions

Use 1/0 (instead of T/F)

Animate Rows

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✓ Truth Table Generated

Embed Truth Table Generator Widget

About Truth Table Generator

What Is a Truth Table?

A truth table is a systematic way to list all possible truth values of a logical expression. For each combination of input variable values (True or False), the table shows the resulting output of the expression. Truth tables are fundamental in:

Digital Logic Design — designing circuits with AND, OR, NOT gates
Computer Science — evaluating conditional expressions and boolean algebra
Philosophy & Mathematics — formal proofs in propositional logic
Software Engineering — testing all branches of conditional logic

How to Use This Truth Table Generator

Enter a boolean expression using variables (A-H) and logical operators. The tool will automatically detect your variables and generate the complete truth table showing all possible input/output combinations.

Use single uppercase letters (A, B, C, ..., H) as variables — up to 8 variables supported
Use parentheses ( ) to control operator precedence
Click the operator buttons or type operators directly
Toggle "Show Sub-expressions" to see intermediate calculation steps

Operator Precedence (Highest to Lowest)

When no parentheses are used, operators are evaluated in this order:

NOT (!, ~, ¬) — evaluated first (highest precedence)
AND (&&, &, ∧) — evaluated second
NAND — evaluated third
XOR, XNOR (^, ⊕, ⊙) — evaluated fourth
OR (||, |, ∨) — evaluated fifth
NOR — evaluated sixth
IMPLIES (→, =>) — evaluated seventh
BICONDITIONAL / IFF (↔, <=>) — evaluated last (lowest precedence)

Supported Operator Syntax

Operator	Accepted Syntax	Description	Example
AND	AND, &&, &, ∧, ·	True only when both operands are true	`A AND B`
OR	OR, \|\|, \|, ∨, +	True when at least one operand is true	`A OR B`
NOT	NOT, !, ~, ¬	Inverts the truth value	`NOT A`
XOR	XOR, ^, ⊕	True when operands differ	`A XOR B`
NAND	NAND	Negation of AND	`A NAND B`
NOR	NOR	Negation of OR	`A NOR B`
XNOR	XNOR, ⊙	True when operands are the same	`A XNOR B`
IMPLIES	→, =>, IMPLIES	False only when P is true and Q is false	`A → B`
BICONDITIONAL	↔, <=>, IFF	True when both have the same value	`A ↔ B`

Understanding Minterms and Maxterms

Minterms are the rows where the output is 1 (True). The Sum of Minterms (SOP) expresses the function as an OR of AND terms. Maxterms are the rows where the output is 0 (False). The Product of Maxterms (POS) expresses the function as an AND of OR terms. Both forms are essential in digital logic simplification and Karnaugh map analysis.

Reference this content, page, or tool as:

"Truth Table Generator" at https://MiniWebtool.com/truth-table-generator/ from MiniWebtool, https://MiniWebtool.com/

Truth Table Generator uses standard boolean algebra rules. For more information, see Truth table - Wikipedia.

Developer API available: Run this tool from your app, automation, or agent with one JSON HTTP request. View API docs

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