Truth Table Generator
Generate complete truth tables for any Boolean logic expression instantly. Enter expressions using AND, OR, NOT, XOR, NAND, NOR, XNOR, implication (→), and biconditional (↔) with up to 8 variables. Compare multiple expressions side by side, detect tautologies and contradictions, and toggle between T/F and 1/0 display — all running locally in your browser with no signup required.
Enter one or more Boolean expressions separated by commas to generate a complete truth table. Supports AND, OR, NOT, XOR, NAND, NOR, XNOR, implication (→), and biconditional (↔).
Operators: AND OR NOT XOR NAND NOR XNOR -> <-> · Also: && || ! ^
Quick Examples
∧AND / && / & — Both true∨OR / || / | — At least one true¬NOT / ! / ~ — Negation⊕XOR / ^ — Exactly one true↑NAND — NOT AND↓NOR — NOT OR⊙XNOR — Both same→-> — Implication↔<-> — BiconditionalWhy Use Our Truth Table Generator?
Instant Truth Table Generation
Enter any Boolean expression and generate a complete truth table instantly. The truth table generator parses your expression in the browser and produces all 2ⁿ input combinations with correct outputs — no loading, no server round-trip.
Secure Truth Table Generator Online
The truth table generator runs entirely in your browser. Your Boolean expressions, logic formulas, and homework problems are never sent to any server — no data collection, no tracking, completely private.
Truth Table Generator — No Installation
Use the truth table generator directly in any modern browser with no downloads, apps, or plugins required. Supports AND, OR, NOT, XOR, NAND, NOR, XNOR, implication (→), and biconditional (↔) with up to 8 variables.
100% Free with Multi-Expression Support
The truth table generator is completely free with no signup, no usage limits, and no ads. Enter multiple comma-separated expressions to compare them side by side in a single table — perfect for verifying logical equivalences and De Morgan's laws.
Common Use Cases for Truth Table Generator
Computer Science Coursework
Students use the truth table generator to complete discrete mathematics and digital logic assignments. Enter any Boolean expression from your textbook and instantly verify your hand-calculated truth table against the generator's output.
Verifying Logical Equivalences
Use the truth table generator to prove or disprove logical equivalences by entering both expressions as comma-separated inputs. If the output columns match for all rows, the expressions are logically equivalent — perfect for verifying De Morgan's laws and distributive properties.
Digital Circuit Design
Hardware engineers use the truth table generator to define the expected behavior of combinational logic circuits before implementation. Generate truth tables for half adders, full adders, multiplexers, and custom gate combinations.
Tautology and Contradiction Detection
The truth table generator automatically detects tautologies (always true) and contradictions (always false) and displays a clear badge. This is useful for verifying logical axioms, checking proof steps, and identifying redundant conditions in code.
Programming and Conditional Logic
Developers use the truth table generator to reason about complex boolean conditions in code. Map your if-statement variables to A, B, C and enter the condition to see all possible input combinations and their outcomes before writing the code.
Teaching and Classroom Demonstrations
Educators use the truth table generator to demonstrate Boolean algebra concepts in real time. The quick-example presets cover AND, OR, NOT, XOR, NAND, NOR, De Morgan's laws, and the half adder — ready to use without any setup.
Understanding the Truth Table Generator
What is a Truth Table?
A truth table is a mathematical table used in logic to determine the output of a Boolean expression for every possible combination of input values. For n variables, a truth table has 2ⁿ rows — one for each unique combination of TRUE and FALSE inputs. Truth tables are fundamental to Boolean algebra, digital circuit design, propositional logic, and computer science. They are used to verify logical equivalences, prove tautologies, identify contradictions, and define the behavior of logic gates. Our truth table generatorparses any Boolean expression written in standard notation and produces the complete truth table instantly in your browser — no server, no account, no waiting.
How Our Truth Table Generator Works
- Enter Your Boolean Expression: Type one or more Boolean expressions into the input field, separated by commas. Use variable names A–Z and any supported operator. The truth table generator automatically extracts all unique variables and sorts them alphabetically as column headers.
- Instant Browser-Based Parsing:Click “Generate Truth Table” and the truth table generator tokenizes and parses your expression using a recursive descent parser entirely in your browser. No expression data is sent to any server — your logic formulas stay completely private on your device.
- Review the Complete Table: The truth table generator displays all 2ⁿ rows with input columns (grey) and output columns (highlighted). TRUE values appear in green, FALSE in red. Toggle between T/F and 1/0 display. Multiple expressions appear as side-by-side output columns for easy comparison.
Supported Operators and Syntax
- AND (∧): Write
AND,&&, or&— outputs TRUE only when both inputs are TRUE. - OR (∨): Write
OR,||, or|— outputs TRUE when at least one input is TRUE. - NOT (¬): Write
NOT,!, or~— negates the input. Can be chained:NOT NOT A. - XOR / NAND / NOR / XNOR / → / ↔: Write
XOR,NAND,NOR,XNOR,->(implication), or<->(biconditional). Parentheses are fully supported for grouping.
Operator Precedence
The truth table generator evaluates operators in the following precedence order (highest to lowest): NOT (highest) → NAND / XNOR → AND → NOR →XOR → OR → IMPLIES (→) →IFF (↔) (lowest). Use parentheses to override precedence — for example, NOT (A AND B) is different from NOT A AND B. When in doubt, always use parentheses to make your intent explicit.
Related Tools
Age Calculator
Calculate your exact age in years, months, weeks, days, hours, and minutes from your date of birth. See alternative age measurements (total days, hours, seconds), zodiac signs, next birthday countdown, and key life milestones. Free online age calculator — no signup required.
Date Difference Calculator
Calculate date differences online for free with our date difference calculator. Instantly find days, weeks, months, and years between any two dates. Accurate, fast, and no signup required.
Date Add / Subtract Calculator
Add or subtract days, weeks, months, years, hours, minutes, and seconds from any date. Support for weekdays/business days calculations. Free online date calculator — no signup required.
Days Until / Days Since Calculator
Calculate exact days, weeks, months, or years until a future event or since a past milestone. Save custom events to your dashboard. Free online date counter — no signup required.
Frequently Asked Questions About Truth Table Generator
A truth table generator is a tool that automatically produces a complete truth table for any Boolean logic expression. It evaluates the expression for every possible combination of TRUE and FALSE input values. Our truth table generator runs entirely in your browser, supports 9 operators, and requires no signup.
Type your expression using variable names A–Z and operators like AND, OR, NOT, XOR, NAND, NOR, XNOR, -> (implication), and <-> (biconditional). You can also use symbols: && for AND, || for OR, ! or ~ for NOT, ^ for XOR. Use parentheses for grouping. Example: (A AND B) OR NOT C.
Absolutely. The truth table generator runs entirely in your browser. Your Boolean expressions, logic formulas, and homework problems are never sent to any server, stored in a database, or tracked. Everything stays completely private on your device.
Yes — the truth table generator is 100% free with no signup, no account, and no usage limits. Generate truth tables for any expression with up to 8 variables as many times as you need, completely free forever.
The truth table generator supports up to 8 variables (A–H or any 8 single letters), which produces a maximum of 256 rows (2⁸). Beyond 8 variables, the table would have 512+ rows and become impractical to read. For most logic problems, 2–4 variables (4–16 rows) is the typical range.
Yes. Enter multiple Boolean expressions separated by commas and the truth table generator will display them as side-by-side output columns in a single table. This is perfect for verifying logical equivalences — if two expressions have identical output columns, they are logically equivalent.
A tautology is a Boolean expression that is TRUE for every possible combination of input values. The truth table generator automatically detects tautologies and displays a green badge when all output values in a single-expression table are TRUE. Similarly, a contradiction (always FALSE) is flagged with a red badge.
Precedence from highest to lowest: NOT → NAND/XNOR → AND → NOR → XOR → OR → IMPLIES (→) → IFF (↔). This follows standard Boolean algebra conventions. Use parentheses to override precedence — for example, NOT (A AND B) differs from NOT A AND B.
Yes. Use -> for logical implication (A → B, which equals NOT A OR B) and <-> for biconditional (A ↔ B, which equals A XNOR B). These are displayed with the standard logical symbols → and ↔ in the table header. Example: A -> B, NOT A OR B will show both expressions are equivalent.