The Basic of Logic Design

Boolean Algebra

- Boolean algebra deals with the values 0 (False) and 1 (True).

- three basic Boolean operations are AND operator, OR operator, and NOT operator.

- can also be defined arithmetically as follows :

	x∧y	=	xy
	x∨y	=	x + y − xy
	¬x	=	1 − x

- can be tabulated with truth table as shown below :

  

 

Boolean Algebra Law :

T1 : Commutative Law

(a) A + B = B + A
(b) A B = B A

 

T2 : Associate Law

(a) (A + B) + C = A + (B + C)
(b) (A B) C = A (B C)

 

T3 : Distributive Law

(a) A (B + C) = A B + A C
(b) A + (B C) = (A + B) (A + C)

 

T4 : Identity Law

(a) A + A = A
(b) A A = A

 

T5 : Simplification Theorem

(a)
(b)  

(c)
(d)

(e) A + A B = A
(f) A (A + B) = A

 

T6 : Identity Law

(a) 0 + A = A
(b) 0 A = 0

 

T7 : Zero And One Laws

(a) 1 + A = 1
(b) 1 A = A

 

T8 : Inverse Law

(a)
(b)  

T9 : De Morgan's Theorem

(a)
(b)