Boolean Algebra Simplification 2019 – Boolean Algebra Theorems

Hello, friends today I am here to give you some knowledge about Boolean Algebra. This is useful in many sectors. Especially in Digital Logic subject. Today I will share knowledge on Boolean Algebra Simplification 2019, Boolean Algebra Theorems and also about Boolean Expression itself.

What Is Boolean Expression or Boolean Algebra Simplification ?

In simple word, Boolean Expression is the mathematics of digital system. And the basic knowledge of Boolean Algebra or Boolean Expression indispensable to the study and analysis of logic circuits of the computer.

The Variable, Complement and Literal are terms which we use in Boolean Algebra or Boolean Expression. 

  1. Variable: The variable is the symbol which is used to represent an action, condition, or any data. The variable can have only the value 0 or 1.
  2. Complement: And the complement is the inverse of the variable and we indicate it by a bar over the variable.
  3. Literal: And the literal term is  the complement of the variable.

Boolean Algebra Simplification :

Boolean Algebra Simplification 2019 – Boolean Algebra Theorems
Boolean Algebra Simplification 2019 – Boolean Algebra Theorems

There are lots of processes to solve a Boolean Algebra. And this process is  Boolean Algebra Simplification. There are some well-developed laws and rules which everyone must keep in mind before solving or while Boolean algebra simplification.

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There are three types of law which we use while solving a Boolean Algebra. We must follow these three rules to solve a Boolean expression. The three laws are given below:

  • Commutative Laws : This is the law for addition of two variables. We can write it as :

A + B = B + A


  • Associative Laws : This associative law is used for three variables. And it can be written as :

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

A (BC) = (AB) C

  • Distributive Laws :  We use this theorem for three variables. It is below :

A (B + C) = AB + AC

Boolean Algebra Theorems

As other calculations, Boolean Algebra has also many theorems. These theorems are like rules that are used to solve Boolean expressions. Boolean Algebra Theorems are given below with examples.

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Demorgan’s Theorems :

Demorgan was the person who know Boole. He has made two theorems that play a good role in Boolean Expression.

The first theorem of Demorgan states that, the complement of a product of variables is equal to the sum of the complements of the variables.

And the second law is the complement of a sum of variables is equal to the product of the complement of the variables.


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