Truth Table Generator

Enter any boolean expression using variables A-Z. The tool generates a full truth table with all input combinations and evaluates each sub-expression step by step.

Supported Operators

Operator	Aliases	Symbol	Description
`AND`	`&&`, `&`, `*`	∧	True when both operands are true
`OR`	`\|\|`, `\|`, `+`	∨	True when at least one operand is true
`NOT`	`!`, `~`	¬	Negates the operand
`XOR`	`^`	⊕	True when operands differ
`NAND`		↑	NOT AND
`NOR`		↓	NOT OR
`XNOR`	`XAND`	⊙	True when operands are equal
`IMP`	`IMPLIES`, `->`	→	Logical implication (NOT A OR B)
`IFF`	`<->`	↔	If and only if (XNOR)

How It Works

The parser tokenizes your input, then builds an abstract syntax tree (AST) using recursive descent parsing. Operator precedence from highest to lowest: NOT, AND / NAND, XOR / XNOR / IFF, OR / NOR, IMP. Parentheses override precedence as expected.

All variables found in the expression are extracted and sorted. The table shows 2ⁿ rows for n variables, covering every possible input combination. Sub-expressions are shown as intermediate columns so you can follow the evaluation step by step.

Boolean Logic Basics

AND: Both A and B must be true for A AND B to be true. Used in conjunction logic.
OR: At least one of A or B must be true. Used in disjunction logic.
NOT: Flips the value. NOT true = false, NOT false = true.
XOR: Exclusive OR. True only when inputs differ, used in half-adders and parity circuits.
NAND / NOR: Universal gates. Any logic circuit can be built from only NAND or only NOR gates.
De Morgan's Laws: NOT (A AND B) = NOT A OR NOT B; NOT (A OR B) = NOT A AND NOT B.

Embed This Util

You can embed this util on your own site as a widget. Adding ?embed=1 to the URL loads a compact version with just the tool itself; no header, menu, or documentation. Paste this snippet into your HTML:

Copy snippet Adjust the height to taste.

Feedback

Help us improve this page by providing feedback, and include your name/email if you want us to reach back. Thank you in advance.

Share with