Which operators are supported?

NOT (!), AND (&), OR (|), XOR (^), NAND (@), NOR (#) and XNOR (%), plus parentheses for grouping. The words AND, OR, NOT and XOR are accepted too, so “A AND NOT B” works the same as “A & !B”.

How many variables can I use?

Up to 8 single-letter variables (A–H style), which produces a 256-row table. Variable letters are case-insensitive, so A and a refer to the same input.

What does operator precedence look like?

NOT binds tightest, then AND, then XOR/XNOR, then OR/NOR — matching standard boolean algebra. Use parentheses whenever you want to override the default order.

Can I use multi-letter variable names?

No — each variable is a single letter (A–H, case-insensitive). This keeps the parser unambiguous so that, for example, AB is read as A AND B rather than one variable named “AB”.

How do I check if two expressions are equivalent?

Generate the table for each one and compare the result columns. If every row matches, the expressions are logically equivalent for all inputs.

What does the result column represent?

It is the value of your whole expression for the inputs in that row. A column that is all 1s is a tautology; all 0s is a contradiction.

Truth Table Generator

Type a boolean expression and instantly see its full truth table for every input combination — all evaluated locally in your browser.

Updated June 2026

Files never leave your browser

Boolean expression

Operators: ! NOT · & AND · | OR · ^ XOR · # NOR · @ NAND · % XNOR. Words AND/OR/NOT/XOR and parentheses also work.

Truth table (8 rows)

A	B	C	A & (B \| !C)
0	0	0	0
0	0	1	0
0	1	0	0
0	1	1	0
1	0	0	1
1	0	1	0
1	1	0	1
1	1	1	1

How to use Truth Table Generator

The Truth Table Generator evaluates any boolean expression across every possible combination of its inputs and lays the results out in a clear table, instantly in your browser. Type an expression using variables A–H and operators such as AND, OR, NOT and XOR, and the tool computes a row for each of the 2ⁿ input combinations. It is the fastest way to verify digital-logic homework, reason about a complex if-condition, or confirm that two boolean formulas are equivalent without reaching for pencil and paper.

Type a boolean expression using variables A–H.
Combine them with operators: ! for NOT, & for AND, | for OR, ^ for XOR.
Use parentheses to group sub-expressions where needed.
Read the generated truth table — one row per input combination.
Copy the table as Markdown to paste into docs or homework.

Your data never leaves your device — 100% private processing.

Operators and precedence

The generator recognises the full set of common boolean operators so you can write expressions naturally. NOT can be written as ! or the word NOT and binds most tightly. AND (& or the word AND) is next, followed by the exclusive operators XOR (^) and XNOR (%), and finally the inclusive operators OR (| or the word OR) and NOR (#). NAND is written as @. When operators of different precedence appear together the tighter one is applied first, so A | B & C is read as A | (B & C). Whenever the default order is not what you mean, wrap the part you want evaluated first in parentheses to make the intent explicit and unambiguous.

Supported boolean operators
Operator	Symbol	Word	Meaning
NOT	!	NOT	Negation — true becomes false
AND	&	AND	True only when both sides are true
OR	\|	OR	True when at least one side is true
XOR	^	XOR	True when the sides differ
NAND	@	—	Negated AND
NOR	#	—	Negated OR
XNOR	%	—	True when the sides are equal

How rows are ordered

Variables are detected automatically, de-duplicated and sorted alphabetically, then used as the table columns. The rows enumerate every combination of those inputs in standard binary-counting order: the first row sets all variables to 0 (false) and the last sets them all to 1 (true), with the right-most variable toggling fastest. For n variables this produces exactly 2ⁿ rows — two variables give four rows, three give eight, and so on up to the eight-variable, 256-row limit. Presenting the inputs in this canonical order makes it easy to compare two tables side by side or to spot patterns such as a column that always matches another.

Worked examples

Simple AND

Inputs: A & B

Result: Four rows; result is 1 only when A=1 and B=1.

Grouped expression

Inputs: A & (B | !C)

Result: Eight rows across variables A, B and C.

Glossary

Truth table: A table listing the output of a boolean expression for every possible combination of its input values.
Boolean expression: A formula combining true/false variables with logical operators that evaluates to true or false.
Operator precedence: The order in which operators are applied when an expression has no parentheses to force grouping.
XOR: Exclusive OR — an operator that is true exactly when its two operands differ.
Tautology: An expression that is true for every input combination, shown as an all-true result column.

Frequently Asked Questions

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Why use Truth Table Generator?

Evaluate every input combination automatically — no manual row-by-row work
Supports AND, OR, NOT, XOR, NAND, NOR and XNOR plus parentheses
Accepts both symbols (&, |, !, ^) and words (AND, OR, NOT, XOR)
Handles up to 8 variables for a complete 256-row table
Runs entirely client-side, so nothing you type leaves the page

Common use cases

Check digital-logic and discrete-math homework answers
Simplify a tangled if-condition by seeing exactly when it is true
Prove two boolean expressions are equivalent by comparing tables
Design and verify logic-gate circuits before building them
Teach or learn boolean algebra with concrete, generated examples

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