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