What is a truth table?

A truth table lists all possible combinations of input values (True/False) and shows the output of a logical expression for each combination.

What operators are supported?

This tool supports AND, OR, NOT, and XOR. You can also use parentheses to group sub‑expressions.

Digital Logic & Boolean Algebra

Truth Table Generator

Evaluate any Boolean expression with AND, OR, NOT, XOR and variables A, B, C, D. See all input combinations, intermediate sub‑expressions, and the final result.

Boolean Expression

🔹 Operators: AND, OR, NOT, XOR 🔹 Variables: A, B, C, D 🔹 Use parentheses ( ) for grouping

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📖 Understanding Truth Tables

A truth table lists all possible combinations of input values (True/False) for a Boolean expression and shows the output for each combination. It's fundamental to digital logic design, computer architecture, and programming.

🔗 Learn more: Wikipedia – Truth table | Boolean algebra

🧮 Operators Reference

AND – output is 1 only if all inputs are 1.
OR – output is 1 if at least one input is 1.
NOT – output is the opposite of input (1 → 0, 0 → 1).
XOR – output is 1 if inputs are different (1 if odd number of 1s).

🧠 How to Write Expressions

Use uppercase variables: A, B, C, D
Operators: AND, OR, NOT, XOR
Example: (A AND B) OR (NOT C)
Nested parentheses: (A XOR B) AND (C OR NOT D)

💡 Real‑World Applications

Truth tables are used in designing digital circuits (CPU logic gates), programming conditionals, database query optimisation, and artificial intelligence rule‑based systems.