Truth Table Generator

Enter a logic (Boolean) expression to get its truth table, canonical forms, a simplified expression and a Karnaugh map. Use it to check answers for digital logic or discrete mathematics exercises.

How to use

1. Type an expression such as A'B + AB' + C in "Logic expression". Open "Operators and notations" to see the symbols you can use.
2. The "Truth table" appears at once, with whether the expression is a tautology. "Values" switches between 1 / 0 and T / F.
3. Under "Forms", read the simplified sum of products and product of sums. With 4 variables or fewer, the "Karnaugh map" shows the groups.
4. Put a "Second expression" under "Check equivalence" to compare two expressions, or press "Copy table" or "Copy LaTeX".

How it works

• Variables are single letters A–Z, up to 6. Letters written together mean AND, so AB is A AND B.
• Binding order, strongest first: NOT, AND, XOR, OR, implies, if and only if. Use parentheses when in doubt.
• Simplification uses the Quine–McCluskey method. If the search runs too long it stops early, and a note says the result may not be the shortest.

Questions and answers

How many rows does a truth table have?

With n variables it has 2 to the power of n rows: 8 rows for 3 variables, 16 for 4 and 64 for 6.

How do I simplify a Boolean expression?

Combine terms that differ in one variable only. AB + AB' is true whenever A is true, whatever B is, so it simplifies to A.

What is the difference between a minterm and a maxterm?

A minterm is a row where the result is 1, written as an AND of all variables; a maxterm is a row where the result is 0, written as an OR. Minterms joined by OR give the canonical SOP.

Can I check De Morgan's laws?

Yes. Enter ¬(A ∧ B) ↔ (¬A ∨ ¬B) and it is shown as a tautology. You can also put the two sides into "Check equivalence" separately.