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Boolean Algebra Calculator

Enter your boolean expression and click “CALCULATE” to simplify it and generate a truth table.

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Enter Expressions:

A(B+C)=AB+AC

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Boolean Algebra Calculator

The Boolean algebra calculator helps simplify Boolean expressions step by step. You can input logical expressions using variables and operators, and the calculator generates truth tables, logical circuits, and output graphs automatically.

What is Boolean Algebra?

Boolean algebra is a branch of mathematics in which variables can take only two values: true (1) or false (0). It uses basic logical operators like AND, OR, and NOT to process truth values. Boolean algebra is also called binary algebra or logical algebra.

How to Use a Boolean Algebra Calculator

1️⃣ Enter the Expression

Type your Boolean expression in the input box of the Boolean algebra calculator.

2️⃣ Use Special Symbols (if needed)

Use ! for NOT
Use + for OR
Use direct letters like AB for AND (A AND B)
Use left (◀) and right (▶) buttons to navigate and edit your expression

3️⃣ Click the Calculate Button

After entering your expression, click "CALCULATE" to simplify it, generate a truth table, or visualize the result.

Basic Logic Operators

Name	Algebraic Function
AND	F = A · B
OR	F = A + B
NOT	F = A'
NAND	F = (AB)'
NOR	F = (A + B)'

Example: Truth Table

Find the truth table for the Boolean expression (A + C) · B

Solution:

Step 1: Break the expression into smaller operations:

D = A + C
Output = D · B

A	B	D = A + C	Output = D · B
0	0	0	0
0	1	0	0
1	0	1	0
1	1	1	1

Simplifying Boolean Expressions

Use a Boolean algebra simplifier calculator to reduce complex logic expressions. This reduces circuit complexity and improves efficiency. The simplification follows Boolean algebra laws:

Laws of Boolean Algebra

Commutative Law: A + B = B + A, A · B = B · A
Associative Law: (A + B) + C = A + (B + C), (A · B) · C = A · (B · C)
Identity Law: A + 0 = A, A · 1 = A
Zero and One Law: A · 0 = 0, A + 1 = 1
Complement Law: A + A' = 1, A · A' = 0
Idempotent Law: A + A = A, A · A = A
Absorption Law: A + (A · B) = A, A · (A + B) = A
Distributive Law: A · (B + C) = (A · B) + (A · C), A + (B · C) = (A + B) · (A + C)
De Morgan's Law: (A + B)' = A' · B', (A · B)' = A' + B'
Double Negation: (A')' = A

Applications of Boolean Algebra Calculator

Digital electronics
Computer programming
Mathematics and set theory
Search engines and databases
Control systems
Networking (routing and switching)
Arithmetic logic units (ALUs)
Error detection and correction
Database query optimization

Truth Table for Binary Logical Operations

The calculator can generate full truth tables for all basic binary operations: AND, OR, NOT, NAND, NOR, XOR, XNOR.

FAQs

What is the importance of this Boolean algebra calculator?

It simplifies logic expressions, generates truth tables, reduces circuit complexity, and saves time and effort.

What is a logic gate?

A logic gate is a digital circuit component that performs a Boolean function, taking one or more binary inputs and producing a single binary output. Common types include AND, OR, NOT, NAND, NOR, XOR, and XNOR.