What is Boolean Algebra

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.

3. Distributive Law

                (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.