Introduction of Boolean Postulates and laws:
Boolean algebra is a type of algebra, invented by a mathematician George Boole in the year 1854. The term “Boolean Algebra” was first suggested by Sheffer in 1913. This algebra is used in digital electronics to simplify the design of the logic gates. It is also used in many modern programming languages. The values of the variables used in Boolean algebra are logic values ‘1’ and ‘0’.
Some set of rules and laws are used in Boolean algebra which is called as ‘Laws of Boolean algebra’. These laws and rules are used to reduce the number of gates used in logic operations. In this algebra the alphabets A,B,C is used as variables and its value can be 1,0 and nothing.
Boolean Postulates and laws:
1) Commutative law:
Interchanging the order of the operands in the Boolean expression gives the same result and does not change the results.
a) A+B=B=A
b) A*B=B*A
2) Associative law:
When AND, OR operation is done on more than two variables, the grouping of the variables does not matter.
a) (A+B)+C= A+(B+C)
b) (A*B)*C= A*(B*C)
3) Distributive law:
a) A*(B+C)= (A*B)+(A*C)
b) A+(B*C)= (A+B)*(A+C)
In the above law A variable is distributed across the grouped variables. The results remain same when AND, OR operation done separately or distributed.
4) Identity law:
a) A+0 = A
b) A*1 = A
When the OR operation is done with ‘0’ and a variable the result is the variable. In the same way when AND operation is done with ‘1’ and a variable the result is the variable.
5) Complement law:
a) A+A1=1
b) A*A1=0
When the OR operation is done with a variable and its complement, the result is ‘1’ . In the same way when AND operation is done with a variable and its complement the result is ‘0’.
6) Idempotent law
a) A+A=A
b) A*A=A
The meaning of the word ‘Idem’ in latin is same and potent means power. So the meaning is having same power. For example in the logical expressions when used A instead of A+A it does not have any additional effect.
7) Absorption law
a) A*(A+B)=A
b) A+(A*B)=A
The AND, OR operation are absorbed and replaced with a variable.
8) Double negation law
((A)1)1 = A
If the variable is negotiated two times the result is the variable remains the same.
9) Annulment law
a) A+1= 1
b) A*0= 0
Annul means null. Thus the AND,OR operation are nullified and replaced with 1 and 0.
0 Comments