A truth table is a mathematical table used in logic—specifically in Boolean algebra, Boolean functions, and propositional calculus—to compute the functional values of logical expressions on each combination of truth values taken by their propositional variables.
In simpler terms, a truth table lists all possible true/false combinations for the variables in a logical statement and shows the resulting truth value of the entire statement for each combination. They are fundamental tools for analyzing and understanding logical circuits, computer programming conditions, and philosophical arguments.
How to Use the Truth Table Calculator
Our Truth Table Generator simplifies the process of creating truth tables for complex logical expressions. Follow these steps:
Enter Your Expression: Type your logical expression into the "Logical Expression" input field.
Supported Operators:
AND (or &&)
OR (or ||)
NOT (or !)
XOR (or ^)
Parentheses ( ) for grouping.
Variables should be single uppercase letters (A-Z). The calculator will automatically identify them.
Generate Table: Click the "Generate Truth Table" button.
View Results: The calculator will display a table showing all possible truth value combinations for your variables and the corresponding truth value of your expression.
Examples of Logical Expressions
Here are some examples of expressions you can use:
A AND B (Conjunction)
A OR B (Disjunction)
NOT A (Negation)
A XOR B (Exclusive OR)
(A AND B) OR C (Grouped expression)
NOT (A OR B) (De Morgan's Law example)
A AND (B XOR C)
The calculator will automatically identify the variables (A, B, C, etc.) from your input expression and sort them alphabetically for the table columns.
Why Are Truth Tables Important?
Digital Logic Design: Essential for designing and analyzing digital circuits, such as those found in computers and other electronic devices.
Computer Science: Used in programming to understand conditional statements, loops, and algorithm logic.
Mathematics and Philosophy: Fundamental in propositional logic to determine the validity of arguments and the properties of logical statements.
Problem Solving: Helps in breaking down complex logical problems into manageable parts and visualizing all possible outcomes.
By using this calculator, you can quickly verify your logical reasoning and gain a deeper understanding of how different logical operators interact.
";
return;
} catch (e) {
resultDiv.innerHTML = "Invalid expression or syntax error: " + e.message + "";
return;
}
}
if (variables.length > 6) { // Limit to 6 variables for performance/readability (2^6 = 64 rows)
resultDiv.innerHTML = "Too many variables. Please limit to 6 variables (A-F) for readability.";
return;
}
var numRows = Math.pow(2, variables.length);
var tableHTML = "
";
// Add variable headers
for (var i = 0; i < variables.length; i++) {
tableHTML += "
" + variables[i] + "
";
}
// Add expression header
tableHTML += "
" + expression + "
";
tableHTML += "
";
// Generate truth table rows
for (var i = 0; i < numRows; i++) {
tableHTML += "
";
var tempExpression = processedExpression;
// Determine truth values for current row and substitute into expression
for (var j = 0; j > (variables.length – 1 – j)) & 1 extracts the j-th bit from i
var value = (i >> (variables.length – 1 – j)) & 1;
tableHTML += "
" + value + "
";
// Replace variable in tempExpression with its current value
// Use a regex with global flag to replace all occurrences
var varToReplace = new RegExp(variables[j], 'g');
tempExpression = tempExpression.replace(varToReplace, value);
}
// Evaluate the expression for the current row
var expressionResult;
try {
// eval() is used here in a controlled manner:
// 1. Variables are replaced with 0 or 1.
// 2. Logical operators are converted to JS equivalents (&&, ||, !, ^).
// This limits the potential for arbitrary code execution.
expressionResult = eval(tempExpression) ? 1 : 0;
} catch (e) {
resultDiv.innerHTML = "Error evaluating expression for row " + (i + 1) + ": " + e.message + "";
return;
}
tableHTML += "