Boolean Algebra by AmiraHurriff

BOOLEAN ALGEBRA by AmiraHurriff
  Introduction :
A Boolean algebra is the combination of variables and operators.usually, it has one or more inputs and produces an output in the
Range of 0 and 1.  Laws Boolean Algebra expressions have been created to help reduce the number of logic gates(Boolean equation.
 These are consist of Boolean Algebra Laws:
•             commutative laws
•             Associative laws
•             Distributive laws
•             Identity laws
•             Zero and one laws
•             Inverse laws
•             DeMorgan’s laws

Types of law	AND form (gates)	OR form (gates)
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
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)
DeMorgan’s Law	(A’.B’)= A’ + B’	(A’ + B’)= A’.B’

 
De Morgan’s laws:
1.  Two separate terms NOR´ed together is the same as the two terms inverted (Complement) and AND´ed for example, A’+B’ = A’∙ B’.
2. Two separate terms NAND´ed together is the same as the two terms inverted (Complement) and OR´ed for example, A’∙B’ = A’ +B’.