Logic Gates and Laws like Commutative,Distributive,Associative etc.

@sheldoncooper-KRWqFp • Oct 27, 2024

Oct 27, 2024

5.2K

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

Like 0 Replies 9

Replies

Welcome, guest

Join CrazyEngineers to reply, ask questions, and participate in conversations.

CrazyEngineers powered by Jatra Community Platform

nareshkumar6539

@nareshkumar6539-BKuVbx • Nov 21, 2011

1)Every logic gate follows Commutative law.
2)AND,OR,Ex-OR,EX-NOR follows Associative law. NAND,NOR doesn`t follow Associative law.
3)AND ,OR follows Distributive law.Ex-OR,EX-NOR,NAND,NOR doesn`t follow Distributive law.AND operation only distributive on EX-OR operation no other operation is distributive including itself.
0
SheldonCooper

@sheldoncooper-KRWqFp • Nov 22, 2011

Can 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.
0
nareshkumar6539

@nareshkumar6539-BKuVbx • Nov 22, 2011

Here i am giving an example for EX-OR which follows associative law.Associative law means order of operation doesn`t change the result.Here i am taking * as an EX-OR 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)`[EX-NOR]
R.H.S=(b`*c)[EX-NOR]
NOTE:- a`*b=a*b`=EX-NOR
2) if one logical gate follows some rule then its duality also follows that rule so EX-NOR also follows the associative law
I hope you will get a little bit idea
0
SheldonCooper

@sheldoncooper-KRWqFp • Nov 22, 2011

nareshkumar6539
put a=1 in that case
L.H.S=(b*c)`[EX-NOR]
R.H.S=(b`*c)[EX-NOR]
NOTE:- a`*b=a*b`=EX-NOR
2) if one logical gate follows some rule then its duality also follows that rule so EX-NOR also follows the associative law
I haven't understood this part.
0
SheldonCooper

@sheldoncooper-KRWqFp • Nov 22, 2011

Ok.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.
0
nareshkumar6539

@nareshkumar6539-BKuVbx • Nov 22, 2011

1)Complement of EX-OR [(b*c)`]gate is EX-NOR
2)In EX-OR operation any one of the input is in complement form then it will act as EX-NOR [ a`*b=a*b`=EX-NOR]
3)In EX-OR operation two inputs are complement then it equal to EX-OR operation only. [a`*b`=EX-OR]
0
nareshkumar6539

@nareshkumar6539-BKuVbx • Nov 22, 2011

Up 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 ,EX-OR,EX-NOR doesn`t follow Distributive law. Except AND no other operation is distributive on EX-OR including itself.
A.(B*C)=(A.B)*(A.C) [Here i am taking * as EX-OR 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
0
SheldonCooper

@sheldoncooper-KRWqFp • Nov 28, 2011

Thanks buddy..It's really helpful.
0
haree

@haree-4I2MQN • Nov 29, 2011

Well done good job .i agree with above post. i think now the time there is no need to further elaborate this.
0