Law of Boolean

Law of Boolean

 1.  Boolean expression is to manipulate them in the same way as normal algebraic expression are manipulated.

 2.  The rules is used to describe circuit whose state can be either, 1(true) or 0(false).

 3.  In order to fully understand this, the relation between the AND­ gate, OR gate and NOT gate operation should be appreciated.

Basic Laws of Boolean Algebra

	AND Form	OR Form
Identity Law	A.1=A	A+0=A
Zero and One Law	A.0=0	A+1=1
Inverse Law	A.A'=0	A+A'=1
Idempotent Law	A.A=A	A+A=A
Commutative Law	A.B=B.A	A+B=B+A
Associative Law	A.(B.C)=(A.B).C	A+(B+C)=(A+B)+C
Distributive Law	A+(B.C)=(A+B).(A+C)	A.(B+C)=(A.B)+(A.C)
Absorption Law	A(A+B)=A	A+A.B=A A+A'B=A+B
DeMorgan’s Law	(A.B)'=A'+B'	(A+B)'=A'.B'
Double Complement Law	X''=X	X''=X

Example 1

 B(A+B)=AB+BB

                   =AB+B              B.B=B

                   =B(A+1)

                   =B                     A+1=1

Example 2

 

 (A+B’+C’)(A+B’C)

       =AA+AB’C+AB’+B’B’C+AC’+B’CC’

       =A(1+B’C+B’+C’)+B’C+B’CC’                        A.A=A

       =A(1+B’)+B’C+B’CC’                                      B’(C+C’)=B’(1)

       =A+B’C(1+C’)                                                 1+B’=1

       =A+B’C                                                            1+C’=1