Calculator Form
Formula Used
Total rows: 2^n, where n is the number of variables.
NOT: reverses a value. AND: true only when both inputs are true. OR: true when at least one input is true.
XOR: true when inputs differ. NAND: inverse of AND. NOR: inverse of OR.
Implication: A -> B = !A OR B. Equivalence: A <-> B is true when both sides match.
Minterms: row numbers where the result is true. Maxterms: row numbers where the result is false.
How to Use This Calculator
- Enter a Boolean expression, such as
(A && B) || !C. - Add a custom variable order if needed.
- Select row order and output style.
- Press the calculate button.
- Review the result table below the header and above the form.
- Use the CSV or PDF buttons to save the table.
Example Data Table
Example expression: (A && B) || !C
| A | B | C | (A && B) || !C |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 |
What Is a Boolean Truth Table?
A Boolean truth table shows every possible input case for a logic expression. It lists each variable first. Then it shows the final result. This makes abstract logic easier to test. Students use it for algebra. Developers use it for conditions. Engineers use it for circuit checks.
Why This Calculator Helps
Manual tables become slow when expressions grow. Three variables already need eight rows. Four variables need sixteen rows. More variables can cause mistakes. This calculator handles those rows automatically. It keeps the order clear. It also shows minterms, maxterms, counts, and expression status.
Supported Logic Ideas
The calculator accepts common operators. Use AND for multiplication logic. Use OR for addition logic. Use NOT for inversion. XOR is true when inputs differ. NAND and NOR are inverted forms. Implication returns false only when a true value leads to false. Equivalence is true when both sides match.
Best Uses in Maths
Truth tables are useful in discrete mathematics. They help prove tautologies. They reveal contradictions. They compare two formulas. They also support set logic and digital design lessons. A complete table removes guessing. Every possible case appears in one place.
Reading the Results
Each input column shows a variable. The last column shows the expression result. A row is true when the full expression is satisfied. The true rows form minterms. The false rows form maxterms. If all rows are true, the expression is a tautology. If no row is true, it is a contradiction. Otherwise, it is a contingency.
Exporting Your Work
The export buttons help save results. CSV works well for spreadsheets. PDF works well for homework, notes, and reports. Always review the entered expression before sharing results. A small operator change can alter the whole table.
Good Input Practice
Use simple variable names. Keep parentheses clear. Write complex formulas in parts first. Then combine them. Check the operator guide when unsure. Clear structure gives better tables and fewer errors.
Accuracy Tips
Start with two variables when learning. Compare a few rows by hand. This builds trust in the output. Save large tables only when needed. Very large tables can be hard to read. Use filters in spreadsheets after export for quick review.
FAQs
1. What is a Boolean truth table?
It is a table that lists every possible input combination for a Boolean expression. Each row shows variable values and the final true or false result.
2. Which operators can I use?
You can use NOT, AND, OR, XOR, NAND, NOR, implication, and equivalence operators. Symbol forms like !, &&, ||, ^, ->, and <-> are also supported.
3. How many rows will the table have?
The number of rows equals 2 raised to the number of variables. For example, three variables create eight rows.
4. What is a tautology?
A tautology is an expression that returns true for every row. Its final result column contains no false values.
5. What is a contradiction?
A contradiction is an expression that returns false for every row. Its final result column contains no true values.
6. What are minterms?
Minterms are row numbers where the expression result is true. They help describe the true cases of a Boolean formula.
7. What are maxterms?
Maxterms are row numbers where the expression result is false. They help describe the false cases of a Boolean formula.
8. Can I export the truth table?
Yes. Use the CSV button for spreadsheet work. Use the PDF button for reports, notes, and homework submissions.