Truth Table Generator

Step 1: Enter Your Boolean Expression

Type your logical expression using variables (A-Z) and operators (AND, OR, NOT, XOR, NAND, NOR, XNOR). For example: "A AND B" or "(A OR B) AND NOT C". Use parentheses to control the order of operations.

Step 2: Generate the Table

Click the "Generate Table" button to create a complete truth table. The tool automatically detects all variables in your expression and generates all possible combinations (up to 6 variables, or 64 rows).

Step 3: Analyze the Results

Review the generated truth table to understand how your logical expression behaves for different input combinations. Each row shows the input values and the corresponding output. Use the copy button to export the table for use in reports or documentation.

Basic Operators

Advanced Operators

Digital Circuit Design

Truth tables are essential for designing and analyzing digital circuits. Engineers use them to verify logic gate configurations, design combinational circuits like adders and multiplexers, and ensure circuits behave correctly for all input combinations. They're the foundation for creating integrated circuits and microprocessors.

Computer Science Education

Truth tables are taught in computer science courses to help students understand Boolean algebra, logical reasoning, and the fundamentals of computer architecture. They provide a visual way to grasp how computers make decisions using binary logic.

Software Development

Programmers use truth tables to design complex conditional logic, debug boolean expressions, optimize if-else statements, and ensure all edge cases are handled correctly. They're particularly useful for testing functions with multiple boolean parameters.

Logic Simplification

Truth tables help identify equivalent logical expressions and simplify complex boolean formulas. Using techniques like Karnaugh maps (K-maps) based on truth tables, engineers can minimize the number of logic gates needed in a circuit, reducing cost and power consumption.

How many rows are in a truth table?

The number of rows in a truth table is 2^n, where n is the number of variables. For example, 2 variables create 4 rows (2^2), 3 variables create 8 rows (2^3), and 4 variables create 16 rows (2^4). Our tool supports up to 6 variables, generating up to 64 rows.

What is the difference between AND and NAND?

AND returns true only when all inputs are true, while NAND (NOT AND) returns the opposite - it returns false only when all inputs are true. NAND is essentially an AND gate followed by a NOT gate. NAND gates are universal and can be used to build any other logic gate.

Can I use truth tables for more than 6 variables?

While theoretically possible, truth tables become impractical for more than 6 variables due to the exponential growth in rows. Seven variables would require 128 rows, and eight would need 256 rows. For complex expressions with many variables, other methods like Boolean algebra simplification or Karnaugh maps are more efficient.

What is operator precedence in Boolean expressions?

Like arithmetic, Boolean operators have precedence: NOT has the highest priority, followed by AND, then OR. Use parentheses to override default precedence. For example, "A OR B AND C" is evaluated as "A OR (B AND C)", but "(A OR B) AND C" forces the OR operation first.

How do I verify if two expressions are equivalent?

Generate truth tables for both expressions using the same variables. If the output columns are identical for all rows, the expressions are logically equivalent. This is a powerful technique for verifying circuit designs or simplifying complex logical statements.

Building Expressions

• Start simple and add complexity gradually
• Use parentheses liberally to make your intent clear
• Test each part of a complex expression separately
• Use meaningful variable names when documenting your work

Analyzing Results

• Look for patterns in the output column (all 0s, all 1s, alternating)
• Identify which input combinations produce true outputs
• Check edge cases (all inputs true, all inputs false)
• Compare with expected behavior to verify correctness

Common Patterns

• A AND A = A (idempotent law)
• A OR NOT A = 1 (law of excluded middle)
• A AND NOT A = 0 (law of contradiction)
• A XOR A = 0 (anything XOR itself is false)