Boolean Algebra Calculator

With the help of our handy Boolean Algebra Calculator tool, you can easily solve any difficult boolean algebraic expression in seconds. Provide your boolean expression as the input and press the calculate button to get the result as early as possible.

Boolean Algebra Calculator: Evaluating the boolean algebraic expressions is not like solving any other mathematical expressions. It is possible by taking the help of various boolean laws and proper knowledge on them. Without all these, you can simply solve your equation by using our free online boolean algebra calculator tool. From this article, you can find the detailed procedure for computing your questions.

How to Solve Boolean Algebra Expression?

In the following sections you can get the step by step process to solve a boolean expression. Go through the below segments and follow them. Two simple steps to solve the boolean expression is by doing the truth table for each operation and finding the result. Another easy step is right here.

  • Take any boolean expression
  • Know all the Laws of Boolean Algebra
  • Replace the Boolean Algebra Laws at each possible step with proper knowledge
  • Keep on doing the step 3 till you reach a point where you can’t substitute any law
  • The resultant will be your answer with no doubt

Laws of Boolean Algebra

Here, we are providing the basic laws of boolean algebra that assist you when solving the boolean algebra expression.

  • Idempotent Law
  • A * A = A

    A + A = A

  • Associative Law
  • (A * B) * C = A * (B * C)

    (A + B) + C = A + (B + C)

  • Commutative Law
  • A * B = B * A

    A + B = B + A

  • Distributive Law
  • A * (B + C) = A * B + A * C

    A + (B * C) = (A + B) * (A + C)

  • Identity Law
  • A * 0 = 0 and A * 1 = A

    A + 1 = 1 and A + 0 = A

  • Complement Law
  • A * ~A = 0

    A + ~A = 1

  • Involution Law
  • ~(~A) = A

  • DeMorgan's Law
  • ~(A * B) = ~A + ~B

    ~(A + B) = ~A * ~B

  • Redundancy Laws
  • Absorption

    A + (A * B) = A

    A * (A + B) = A

    (A * B) + (A * ~B) = A

    (A + B) * (A + ~B) = A

    A + (~A * B) = A + B

    A * (~A + B) = A * B

Example:

Question: Solve ~(A * B) * (~A + B) * (~B + B)?

Solution:

Given expression is ~(A * B) * (~A + B) * (~B + B)

By applying Complement law i.e ~B + B=1

=~(A * B) * (~A + B) * 1

Apply Identity law i.e (~A + B) * 1=~A + B

=~(A * B) * (~A + B)

Apply DeMorgan's law i.e ~(A * B)=(~A + ~B)

=(~A + ~B) * (~A + B)

Distributive Law is ~A + B=B

=(~A + ~B) * B

Complement law says ~B * B=0

=~A + 0

Apply Identity law

=~A

~(A * B) * (~A + B) * (~B + B)=~A

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Boolean Algebra Calculator

Frequently Asked Questions on Boolean Algebra

1. What is meant by Boolean Algebra?

Boolean algebra is a branch of mathematics that deals with the operations on logical values. It returns only two values i.e true or false or represented by 0 and 1.


2. What are the operations used in the boolean algebra?

The various basic operations used in the boolean algebra are Conjunction (AND), Disjunction(OR), and Negotiation (NOT).


3. How do you calculate the Boolean Algebra Expression using a calculator?

Enter a valid boolean expression and hit on the calculate button to get your answer quickly.


4. What are the 7 logic gates?

There are seven basic logic gates. They are AND, OR, XOR, NOT, NAND, and XNOR.


5. What is the other name of Boolean Algebra?

Boolean Algebra is used to simplify and analyze the digital (logic) circuits. It has only the binary numbers i.e. 0 (False) and 1(True). It is also called Binary Algebra or logical Algebra.