Calculator
Example Data Table
Expression: (A AND B) OR NOT C
| A | B | C | A AND B | NOT C | Output |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 0 | 1 |
Formula Used
The calculator evaluates each row by assigning every possible truth value to each variable.
| Operation | Formula | Meaning |
|---|---|---|
| NOT | ¬A | Reverses the value of A. |
| AND | A ∧ B | True only when both values are true. |
| OR | A ∨ B | True when at least one value is true. |
| XOR | A ⊕ B | True when values are different. |
| NAND | ¬(A ∧ B) | False only when both values are true. |
| NOR | ¬(A ∨ B) | True only when both values are false. |
| Implication | A → B = ¬A ∨ B | False only when A is true and B is false. |
| Equivalence | A ↔ B | True when both values match. |
Canonical sum of products uses all true rows. Canonical product of sums uses all false rows. These forms help analyze minterms, maxterms, and circuit behavior.
How to Use This Calculator
- Enter a Boolean expression in the first field.
- Use operators like AND, OR, NOT, XOR, NAND, NOR, ->, and <->.
- Add a second expression when you want to compare equivalence.
- Enter a variable order if you want a custom column order.
- Select output labels and row order.
- Press the generate button to view the truth table.
- Use CSV or PDF buttons to export the table.
Boolean Algebra Truth Table Guide
Logic Made Visible
Boolean algebra turns logic into a clear table. Each variable can be true or false. A truth table lists every possible input case. It then evaluates the expression for each case. This calculator helps students, teachers, and circuit learners test logic quickly.
Why Truth Tables Matter
Truth tables show how a statement behaves. They make hidden logic visible. You can see when an expression is always true. You can also see when it is always false. This helps with proofs, digital circuits, switching design, and discrete mathematics. A table also helps compare two formulas. If both outputs match in every row, the formulas are equivalent.
Advanced Expression Support
The tool accepts common Boolean symbols. Use AND, OR, NOT, XOR, NAND, NOR, implication, and equivalence. You can type symbols or words. Parentheses control the order of evaluation. The calculator also supports apostrophe notation, such as A' for NOT A. This makes it useful for algebra homework and circuit notation.
Minterms and Maxterms
A minterm represents a row where the final output is true. The list of true rows gives the canonical sum of products. A maxterm represents a row where the final output is false. The list of false rows gives the canonical product of sums. These forms are useful before simplification. They also help when building Karnaugh maps.
Good Learning Practice
Start with small expressions. Check each operator step by step. Then add more variables. Use the compare field to test identities, such as De Morgan laws. Export the table when you need a record. The CSV file is useful for spreadsheets. The PDF file is useful for reports.
Accuracy Notes
Boolean logic uses exact rules. The calculator follows the selected operator precedence. Parentheses are still the safest way to avoid confusion. Very large expressions may create many rows. Every new variable doubles the row count. Use clear variable names and verify the final formula before using it in design work.
Review Benefits
Use the notes beside each result carefully. They explain satisfiable, tautology, and contradiction states. This gives quick feedback before deeper simplification. When a second expression is entered, the match column highlights equivalence. That comparison supports proofs, classroom checks, and early circuit reviews. It also reduces manual checking time well.
FAQs
1. What is a Boolean truth table?
A Boolean truth table lists every possible variable combination. It shows the final output for each row.
2. Which operators can I use?
You can use NOT, AND, OR, XOR, NAND, NOR, implication, and equivalence operators.
3. Can I use symbols instead of words?
Yes. You can use symbols like !, +, *, ^, ->, and <->.
4. What does A' mean?
A' means NOT A. It is common shorthand in Boolean algebra and digital logic.
5. What are minterms?
Minterms are row numbers where the expression output is true. They form canonical SOP notation.
6. What are maxterms?
Maxterms are row numbers where the expression output is false. They form canonical POS notation.
7. How do I compare two expressions?
Enter the second expression in the compare field. The calculator checks every row for matching outputs.
8. Why should I use parentheses?
Parentheses remove ambiguity. They make your intended operator order clear and reduce input mistakes.