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Chapter: Digital Electronics - Minimization Techniques and Logic Gates

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Boolean Postulates and Laws

Investigating the various Boolean theorems (rules) can help us to simplify logic expressions and logic circuits.

BOOLEAN POSTULATES AND LAWS:

 

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 :


 

T6 : Redundance Law

(a)        A + A B = A

 

(b)       A (A + B) = A

 

T7 :

(a)        0 + A = A

 

(b)       0 A = 0

 

T8 :

(a)        1 + A = 1

 

(b)       1 A = A

 

T9 :

 


 


Boolean Theorems

 

Investigating the various Boolean theorems (rules) can help us to simplify logic expressions and logic circuits.


Boolean postulates are                   

— The Commutative Law of addition for two variable.       

         A + B         =       B + A         

— The Commutative Law of multiplication for two  variable.       

         A . B  =  B  . A   

— The Associative law of addition with multiplication is written as       

         A + (B + C) = A +B +C

— The Associative law of multiplication with addition is written as       

         A . (B . C)  = (A . B) . C        

— The Associative law of multiplication with addition is written as       

         A . (B + C)  =  A . B + A . C  

— The Associative law of addition with multiplication is written as       

         A + (B . C) = (A + B) . (A + C)       


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