Boolean Algebra Calculator

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Boolean Algebra Calculator

Evaluate logic expressions and truth values

Supported: AND (&, .), OR (|, +), NOT (!, ~), XOR (^), Parentheses ()

1 (True) 0 (False)
1 (True) 0 (False)
1 (True) 0 (False)
Resulting Truth Value
function calculateBoolean() { var expression = document.getElementById('booleanExpression').value.trim(); var valA = document.getElementById('varA').value === "1"; var valB = document.getElementById('varB').value === "1"; var valC = document.getElementById('varC').value === "1"; var resultDiv = document.getElementById('booleanResultWrapper'); var errorDiv = document.getElementById('errorMessage'); var finalResultDisplay = document.getElementById('booleanFinalResult'); var binaryResultDisplay = document.getElementById('booleanBinaryResult'); resultDiv.style.display = 'none'; errorDiv.style.display = 'none'; if (!expression) { errorDiv.innerHTML = "Please enter a logic expression."; errorDiv.style.display = 'block'; return; } try { var processed = expression.toUpperCase(); // Replace Operators with JS equivalents processed = processed.replace(/\bAND\b/g, '&&'); processed = processed.replace(/\./g, '&&'); processed = processed.replace(/\bOR\b/g, '||'); processed = processed.replace(/\+/g, '||'); processed = processed.replace(/\bNOT\b/g, '!'); processed = processed.replace(/~/g, '!'); processed = processed.replace(/\bXOR\b/g, '^'); // Replace variables (using boundaries to avoid partial matches) processed = processed.replace(/\bA\b/g, valA); processed = processed.replace(/\bB\b/g, valB); processed = processed.replace(/\bC\b/g, valC); // Eval the logical expression // Note: ^ in JS is bitwise XOR, works for true/false as 1/0 var result = eval(processed); // Convert truthy/falsy to 1/0 var finalBool = !!result; finalResultDisplay.innerHTML = finalBool ? "TRUE" : "FALSE"; finalResultDisplay.style.color = finalBool ? "#27ae60" : "#c0392b"; binaryResultDisplay.innerHTML = "Binary Output: " + (finalBool ? "1" : "0"); resultDiv.style.display = 'block'; } catch (e) { errorDiv.innerHTML = "Invalid syntax. Ensure you use A, B, C and standard operators correctly (e.g., A AND B)."; errorDiv.style.display = 'block'; } }

Understanding Boolean Algebra

Boolean algebra is a branch of mathematics that deals with variables that have only two distinct values: True (1) and False (0). It forms the foundation of modern digital electronics and computer science, allowing engineers to design complex logic circuits using simple gates.

Core Logical Operators

  • AND (Conjunction): Output is 1 only if all inputs are 1. Represented as A . B or A & B.
  • OR (Disjunction): Output is 1 if at least one input is 1. Represented as A + B or A | B.
  • NOT (Negation): Reverses the input. If A is 1, NOT A is 0. Represented as !A or ~A.
  • XOR (Exclusive OR): Output is 1 only if the inputs are different. Represented as A ^ B.

The Three Fundamental Laws

Law AND Form OR Form
Commutative A . B = B . A A + B = B + A
Associative (A . B) . C = A . (B . C) (A + B) + C = A + (B + C)
Distributive A . (B + C) = (A . B) + (A . C) A + (B . C) = (A + B) . (A + C)

Practical Example

Suppose you are designing a security alarm. The alarm (Result) should ring if the Sensor A (Motion) is triggered AND the System B (Armed) is active. The expression is A AND B. If Motion is detected (A=1) but the system is not armed (B=0), the result is 1 AND 0 = 0 (No alarm).

De Morgan's Theorem

One of the most powerful tools in boolean simplification:

  • NOT (A AND B) = (NOT A) OR (NOT B)
  • NOT (A OR B) = (NOT A) AND (NOT B)

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