Truth Table Generator
Enter a Boolean expression using variables like A, B, and operators like && (AND), || (OR), and ! (NOT).
Truth Table Generator – Free Online Boolean Calculator
Use this free Truth Table Generator to instantly generate truth tables for any Boolean expression. It’s a powerful educational and logic tool for students, programmers, and electronics engineers who want to analyze and understand digital logic circuits, logic gates, and Boolean algebra.
What is a Truth Table?
A truth table is a tabular method used in logic and digital electronics to show all possible combinations of input values and their corresponding output for a given logical or Boolean expression. It helps visualize how logical operators (AND, OR, NOT, XOR) affect results based on different conditions. Also, it helps visualize how a logical operation behaves under every possible combination of true (1) and false (0) inputs.
For example, if you have a logical operation with two inputs, say A and B, the truth table lists all four possible combinations of these inputs (00, 01, 10, 11) and shows the output result for each. Truth tables are fundamental for analyzing, designing, and troubleshooting digital circuits and logical statements, as they clearly illustrate the relationship between inputs and outputs.
Logic Gate Symbols and Their Meaning
| Logic Gate | Symbol (Text) | Boolean Expression | Meaning |
|---|---|---|---|
| AND | &, ∧, ⋅ | A ∧ B | 1 only if both inputs are 1 |
| OR | +, ∨ | A ∨ B | 1 if at least one input is 1 |
| NOT | ¬, ! | ¬A | Inverts the input |
| NAND | ↑ | ¬(A ∧ B) | Opposite of AND |
| NOR | ↓ | ¬(A ∨ B) | Opposite of OR |
| XOR | ⊕ | A ⊕ B | 1 if inputs are different |
| XNOR | ≡ | ¬(A ⊕ B) | 1 if inputs are the same |
Truth Table Example
| A | B | A AND B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Advanced Truth Table Generation
This online truth table calculator supports advanced Boolean expressions using up to 5 variables like A, B, C, D, and E. You can use parentheses for grouping and combine operators to generate complex logical conditions. It’s ideal for digital logic design, gate-level simulations, and Boolean algebra simplification.
How to Use the Truth Table Generator
- Enter your Boolean expression using variables like A, B, C, etc.
- Use operators: && for AND, || for OR, ! for NOT, ^ for XOR.
- Click “Generate” to create the truth table.
- Scroll to see input combinations and final output values.
Frequently Asked Questions (FAQ)
- What is a truth table used for?
- It is used to analyze logic gates and Boolean expressions by showing outputs for all input combinations.
- Can this tool handle multiple variables?
- Yes, it supports expressions with 2 to 5 variables like A, B, C, D, E.
- What operators are supported?
- AND (&&), OR (||), NOT (!), XOR (^), and parentheses ().
- Is this tool free?
- Yes! 100% free and online—no installation needed.
- How many rows will a truth table have?
- 2ⁿ rows for n variables. Example: 3 variables = 8 rows.
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