Boolean Truth Table Maker
Supported operators: NOT, AND, OR, XOR, NAND, NOR, XNOR, implication, and equivalence. Symbols like !, ~, &, |, ^, ->, and <-> also work.
Example Data Table
Sample expression: (A AND B) OR NOT C
| A | B | C | Result |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 |
Formula Used
The calculator evaluates every possible variable assignment and applies Boolean operator rules to the expression. For n variables, the table contains 2n rows.
- NOT P = 1 when P is 0.
- P AND Q = 1 only when both P and Q are 1.
- P OR Q = 1 when at least one input is 1.
- P XOR Q = 1 when inputs differ.
- P NAND Q = NOT(P AND Q).
- P NOR Q = NOT(P OR Q).
- P → Q = NOT(P) OR Q.
- P ↔ Q = 1 when P and Q share the same truth value.
How to Use This Calculator
- Enter a Boolean expression using variables and supported operators.
- Optionally set a custom variable order to control table columns.
- Choose how truth values should appear in the final table.
- Select ascending or descending row order for the combinations.
- Submit the form to build the truth table and chart.
- Use the CSV or PDF buttons to export the visible result.
Frequently Asked Questions
1. What expressions can this calculator evaluate?
It supports named variables, parentheses, constants, and operators such as NOT, AND, OR, XOR, NAND, NOR, XNOR, implication, and equivalence.
2. How many variables can I use?
You can use up to eight variables. That cap keeps the table readable and avoids creating very large result grids.
3. Why does the row count double often?
Each added variable has two possible states, true or false. Because combinations multiply, the total row count becomes 2n.
4. What does implication mean here?
Implication uses the rule P → Q = NOT(P) OR Q. It is false only when P is true and Q is false.
5. Can I export the generated table?
Yes. After generating results, you can download the visible table as a CSV file or create a PDF export from the page.
6. Does variable order affect the result?
Variable order changes the column sequence and the row pattern order, but it does not change the logical meaning of the expression.
7. Can I type symbols instead of words?
Yes. Symbols like !, ~, &, |, ^, ->, and <-> are accepted along with keyword forms such as AND or XOR.
8. Why am I seeing a parsing error?
Parsing errors usually come from missing parentheses, incomplete operators, or mismatched variable order names. Check spacing and operator placement, then try again.