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

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.