About this calculator
How to quickly generate a truth table for a logical expression? A truth table is a basic tool in digital logic and Boolean algebra that lists the output values of a logical expression for all possible input combinations. For an expression with n variables, the truth table has 2ⁿ rows, each row corresponding to an input combination.
Truth tables are indispensable in digital circuit design. When designing a combinational logic circuit, first list the truth table according to the functional requirements, then derive the logic expression, and finally implement the circuit. Truth tables are also used to verify the equivalence of logical expressions, simplify logic circuits, and analyze circuit functions.
In computer science, truth tables are used to understand the behavior of logical operators (AND, OR, NOT, XOR, etc.). In artificial intelligence, truth tables are used for knowledge representation and reasoning. In mathematical logic, truth tables are used to determine the eternal truth, falsehood or satisfiability of propositional formulas.
Our truth table generator can automatically generate a truth table for any logical expression. Supports common logical operators, including AND (AND), OR (OR), NOT (NOT), XOR (XOR), implication (→), equivalence (↔), etc. You can also display the truth values of intermediate steps to help you understand the calculation process of complex expressions.
How to use
Using the truth table generator is very simple. Just enter a logical expression.
**Basic steps:** 1. Enter a logical expression (using variables A, B, C, etc.) 2. Select logical operators (AND, OR, NOT, XOR, etc.) 3. Click the "Generate" button 4. View the complete truth table
**operator means:** • AND (AND): ∧ or & or * • OR (or): ∨ or | or + • NOT (not): ¬ or ~ or ! • XOR (XOR): ⊕ or ^
**Example 1:** Generate a truth table for A AND B. The result shows that the output is true only if both A and B are true.
**Example 2:** Generate a truth table for (A OR B) AND (NOT C). There are 3 variables and 8 lines in total.
**Example 3:** Verify DeMorgan's law: NOT(A AND B) = (NOT A) OR (NOT B). Generate truth tables for the two expressions, compare the last column, and find they are exactly the same, proving equivalence.
Main features
• Various operators: AND, OR, NOT, XOR, NAND, NOR, implication, equivalent • Multi-variable support: supports 2 to 10 variables • Intermediate Steps: Shows intermediate calculation steps of complex expressions • Expression parsing: automatically parses logical expressions • Equivalence verification: Compare two expressions for equality • Always True and Always False: Determine whether the expression is always true or always false. • Main disjunctive normal form: generates the main disjunctive normal form of the expression • Main Conjunctive Normal Form: The main conjunctive normal form of the generated expression • Export function: export truth table as image or text • Totally free: no registration required, use anytime
Use cases
• Digital Logic Learning: Students learn logical operations and truth tables • Circuit design: Design combinational logic circuits based on truth tables • Logical Simplification: Simplify logical expressions through truth tables • Equivalence verification: Verify whether two logical expressions are equivalent • Programming learning: understanding logical operators in programming languages • Mathematical logic: determine the properties of propositional formulas • Exam preparation: Quickly generate truth table verification answers • Teaching aid: Teacher explains the concept of logical operations • Circuit Analysis: Analyzing the logical functionality of existing circuits • Algorithm Design: Design logic-based algorithms