__Boolean Algebra__

### What is Boolean Algebra-?

An algebra which deals with the binary number system is known as Boolean Algebra. In the mathematical algebra we can take any values for variables of A, B, C etc...., but in this Boolean Algebra we can take only to values for the variables that is 0 and 1 only. The Boolean Algebra is used to design digital logic circuit. Boolean Algebra was developed by George Boole.

#### Laws of Boolean Algebra

There are three types of laws are there in Boolean Algebra

**1.**

**Communicative Law:-**This is the law for addition and also for multiplication. We also called it as communicative law of addition and communicative law of multiplication.

**(a)**

**Communicative law of Addition:-**A+B=B+A if we will also change the order of the variables there will be changes will take place, on A+B or B+A we get same result as shown below in a truth table.

**(b)**

**Communicative Law of Multiplication:-**Here the symbol of multiplication is dot (.). A.B=B.A if we will also change the order of the variables there will be changes will take place, on A.B or B.A we get same result as shown below.

**2.**

**Associative Law:-**This is the law for addition and also for multiplication. We also called it as communicative law of addition and communicative law of multiplication.

**(a)**

**Associative Law for Addition:-**A+(B+C)=(A+B)+C if we will also change the order of the variables there will be changes will take place, on A+(B+C) or (A+B)+C we get same result as shown below.

**(b)**

**Associative Law for Multiplication:-**A.(B.C)=(A.B).C if we will also change the order of the variables there will be changes will take place, on A.(B.C) or (A.B).C we get same result as shown below.

**(a)**

**Distributive Law over AND Operator:-**A.(B+C)=A.B+A.C can be distributed.

**(b)**

**Distributive Law over Addition operator or OR Operator:-**A+(B.C)=(A+B).(A+C) can be distributed.

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