Logic Gates and Laws like Commutative,Distributive,Associative etc.
Can anyone explain me,which logic gates follow and don't follow which of the laws like Commutative,Distributive,Associative etc. And how?
Replies

nareshkumar65391)Every logic gate follows Commutative law.
2)AND,OR,ExOR,EXNOR follows Associative law. NAND,NOR doesn`t follow Associative law.
3)AND ,OR follows Distributive law.ExOR,EXNOR,NAND,NOR doesn`t follow Distributive law.AND operation only distributive on EXOR operation no other operation is distributive including itself. 
SheldonCooperCan you derive some of these for associative and distributive laws? Means how can I recall them if I forgot or jumbled? just give me example taking some values.Just give me a hint how can I derive it.I don't want derivation for each and every gate.

nareshkumar6539Here i am giving an example for EXOR which follows associative law.Associative law means order of operation doesn`t change the result.Here i am taking * as an EXOR operator.
a*(b*c)=(a*b)*c Fixed one variable like
put a=0 and check L.H.S and R.H.S if a=0 in the above relation
L.H.S= b*c
R.H.S= b*c
put a=1 in that case
L.H.S=(b*c)`[EXNOR]
R.H.S=(b`*c)[EXNOR]
NOTE: a`*b=a*b`=EXNOR
2) if one logical gate follows some rule then its duality also follows that rule so EXNOR also follows the associative law
I hope you will get a little bit idea 
SheldonCooper
I haven't understood this part.nareshkumar6539put a=1 in that case
L.H.S=(b*c)`[EXNOR]
R.H.S=(b`*c)[EXNOR]
NOTE: a`*b=a*b`=EXNOR
2) if one logical gate follows some rule then its duality also follows that rule so EXNOR also follows the associative law 
SheldonCooperOk.Got Associative and Commutative laws.Now just give me example of distributive law.To show it one must have to use 2 different gates isn't it? So I am stuck with the representation.

nareshkumar65391)Complement of EXOR [(b*c)`]gate is EXNOR
2)In EXOR operation any one of the input is in complement form then it will act as EXNOR [ a`*b=a*b`=EXNOR]
3)In EXOR operation two inputs are complement then it equal to EXOR operation only. [a`*b`=EXOR] 
nareshkumar6539Up to my knowledge in distributive 2 different gates should be there.I think you already know OR, AND gates follows Distributive law.
A.(B+C)=A.B+A.C
A+BC=(A+B).(A+C)
In the previous I mention that NAND,NOR ,EXOR,EXNOR doesn`t follow Distributive law. Except AND no other operation is distributive on EXOR including itself.
A.(B*C)=(A.B)*(A.C) [Here i am taking * as EXOR operator]
Fix one variable
put A=0 then check L.H.S and R.H.S
L.H.S=0
R.H.S=0
put A=1 then check L.H.S and R.H.S
L.H.S=B*C
R.H.S=B*C
like this you can check any of the rule.I hope you get a little bit idea about how to check the particular gate follows the rule or not 
SheldonCooperThanks buddy..It's really helpful.

hareeWell done good job .i agree with above post. i think now the time there is no need to further elaborate this.
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