About the Truth Table Generator
Truth Table Generator builds the truth table of a boolean or logic expression. Type an expression such as A AND (B OR NOT C) using the letters A to Z, the operators AND, OR, NOT, XOR, NAND, NOR, XNOR, IMPLIES and IFF, or the symbols &, |, !, ^, -> and <->, and the page lists every combination of the variables with the result. It also tells you whether the expression is a tautology (always true), a contradiction (always false) or contingent, lists the true rows (minterms) and writes the sum of products. It works for up to six variables.
Updated October 2026
How to use the Truth Table Generator
- 1Type your expression using single letters as variables.
- 2Use AND, OR, NOT and the other operators, or the symbols.
- 3Use brackets to control the order of the operations.
- 4Read the table, the result type and the minterms.
- 5Copy the table as tab-separated text for a spreadsheet.
Reading a truth table
Each row of the table is one scenario: it sets every variable to 1 (true) or 0 (false). The last column shows the result of your expression in that scenario. Reading down the result column tells you when the expression is true. The table is the complete behaviour of a logic circuit or a statement, which is why it is the first thing taught in logic and digital electronics.
Typing expressions
You can type the way you like. The page understands words and symbols side by side, so A AND NOT B and A & !B give the same table. Chains of the same operator are read from left to right, except IMPLIES, which groups from the right. If two letters sit next to each other with no operator, the page asks you to add one rather than guessing.
- A AND (B OR NOT C)
- (A -> B) AND (B -> C)
- NOT (A AND B) IFF (NOT A OR NOT B)
- A XOR B XOR C
Using it to check laws
De Morgan's laws, the distributive law and other identities can be checked by building the table of both sides and comparing the result columns. If the columns match, the expressions are equivalent. This is a quick way to confirm that a simplified circuit does the same job as the original.
Related tools
Work with binary numbers using the Binary Calculator and the Bitwise Calculator, and convert them with the Number Base Converter. The Probability Calculator covers chance rather than logic.
Features
- AND, OR, NOT, XOR, NAND, NOR, XNOR, IMPLIES, IFF
- Words and symbols both accepted
- Up to six variables, 64 rows
- Tautology, contradiction or contingent
- Minterms and sum of products
- Private: nothing is uploaded
Frequently asked questions
What is a truth table?
A table that lists every possible combination of true and false for the variables of an expression and the result of the expression for each one.
What is a tautology?
An expression that is true for every combination, such as A OR NOT A. A contradiction is false for every combination, such as A AND NOT A.
Which operators can I use?
AND (&, ∧, *), OR (|, ∨, +), NOT (!, ~, ¬), XOR (^, ⊕), NAND, NOR, XNOR, IMPLIES (->, →) and IFF (<->, ↔). You can also use 1 and 0, or TRUE and FALSE.
In what order are operators applied?
NOT first, then AND and NAND, then XOR, then OR, NOR and XNOR, then IMPLIES, then IFF. Use brackets whenever you are unsure.
What does A IMPLIES B mean?
It is false only when A is true and B is false, and true otherwise. It equals NOT A OR B.
What are minterms?
Rows where the expression is true, numbered from 0 with the first variable as the highest bit. Their OR gives the canonical sum of products form.
Why six variables at most?
The table doubles with every variable. Six gives 64 rows, which still fits on a page.
Is my expression uploaded?
No. The table is made in your browser.