Truth Table Generator - Boolean Logic Tables
Use this truth table generator to build Boolean logic tables instantly. Enter an expression to see rows, true counts, and classification.
Truth Table Generator
Results
Truth Table
What is a Truth Table Generator?
A truth table generator creates every true-or-false input combination for a logical expression and shows the resulting output for each row. It is useful when a statement has enough variables that manual row building becomes slow or error-prone.
Students use it to check discrete math and computer science homework. Programmers use it to test conditions with several flags. Electronics learners use it to reason through Boolean logic before simplifying gates or circuits.
- • Build complete tables for up to five variables.
- • Compare true rows and false rows at a glance.
- • Identify tautologies, contradictions, and contingencies.
To simplify a related expression, explore our Boolean Algebra Calculator to work with Boolean rules directly.
How the Truth Table Calculator Works
This truth table for Boolean expression tool parses your expression, finds the unique variables, creates 2^n rows, and evaluates the expression in each row. The final column records the result for that exact assignment.
According to the Stanford CS103 Truth Table Tool, propositional formulas can be entered with operators such as /\, &&, not, !, implication arrows, and constants T and F.
To review the 1 and 0 notation used in many tables, use our Binary Converter for quick base conversions.
Key Concepts Explained
Variables
Letters such as A, B, and C stand for propositions that can be true or false.
Operators
AND, OR, NOT, XOR, implication, and biconditional connect variables into a compound statement.
Truth Rows
Each row is one possible assignment of truth values to all variables.
Classification
A table with implication and biconditional operators can still be classified from the final column.
To switch among number systems often used near logic tables, try our Base Converter.
How to Use This Calculator
Enter a Boolean expression such as (A and B) -> C.
Choose whether the truth table calculator should display T/F, 1/0, or true/false.
Keep the variable limit at five unless you want to intentionally block large tables.
Press Calculate and read the generated rows, counts, and expression classification.
To turn counts into shares after you build a table, use our Percentage Calculator.
Benefits of Using This Calculator
- • Avoid missed rows when an expression has three, four, or five variables.
- • Use it as a tautology contradiction contingency checker before writing a proof.
- • Paste notation from class notes, programming examples, or circuit diagrams.
- • See true rows, false rows, and final classification in one compact result.
- • Test implication direction and biconditional equivalence without hand-copying rows.
To solve paired algebraic statements next, use our System of Equations Calculator.
Factors That Affect Your Results
Variable count
The number of rows in a truth table doubles with every added variable, so five variables produce 32 rows.
Operator precedence
NOT is evaluated before AND, OR/XOR, implication, and biconditional unless parentheses change the order.
Parentheses
Parentheses remove ambiguity and are the best way to match a textbook expression or code condition.
Notation style
Words and symbols are accepted, but the expression still has to be complete and syntactically valid.
According to TechTarget, the number of value rows in a truth table is calculated with 2^n, where n is the number of variables in the expression.
To generate sample values for practice problems, try our Random Number Generator.
Truth Table Generator FAQ
Q: How do you make a truth table?
A: List the variables, create 2^n rows, fill in every true-or-false combination, then evaluate the expression on each row. Parentheses and operator precedence determine the order of evaluation.
Q: What is a truth table generator?
A: A truth table generator is a calculator that builds all truth-value combinations for a logical or Boolean expression. It saves time by parsing the expression and evaluating every row automatically.
Q: How many rows are in a truth table?
A: A truth table has 2^n value rows, where n is the number of distinct variables. One variable gives 2 rows, two variables give 4 rows, and five variables give 32 rows.
Q: What does a truth table show?
A: A truth table shows how a logical expression behaves for every possible input combination. The final output column reveals whether the statement is always true, always false, or sometimes true.
Q: What is the difference between tautology and contradiction?
A: A tautology is true in every row. A contradiction is false in every row. A contingency has at least one true row and at least one false row.
Q: Can a truth table use implication and biconditional operators?
A: Yes. This calculator supports implication with -> or => and biconditional with <-> or <=>. It also supports AND, OR, NOT, XOR, parentheses, and true or false constants.