# 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

• nareshkumar6539
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.
• SheldonCooper
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.
• nareshkumar6539
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
• SheldonCooper
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.
• SheldonCooper
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.
• nareshkumar6539
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]
• nareshkumar6539
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
• SheldonCooper
• haree
Well done good job .i agree with above post. i think now the time there is no need to further elaborate this.

You are reading an archived discussion.

## Boolean Algebra problems

1) If z=x*y then z*x is? Options- 1)x 2)0 3)y 4)1 2) How many functions are possible with 'n' binary variables? 3) How many functions are possible with 2 Boolean...

## Is Play Station 4 Coming In 2012?

There's a sudden rise of rumors about the announcement of next Playstation in 2012. Killzone, one of the most popular games on PS platform is said to be under development...

## General Machine Structure - Von neumann Architecture Explained - System Programming

The structure of CPU for a typical Von Neumann Machine is as follows - [Image Courtesy - Donovan Book] The structure above consists of - 1. Instruction Interpreter 2. Location...

## World's Lightest Material @ 0.9 mg/cc!

US scientists stake a claim for the world's lightest material Read more: US scientists stake a claim for the world's lightest material | News | The Engineer ​

## Need Help in superconducting magnetic energy storage system (SMES)

Currently I am working on superconducting magnetic energy storage system (SMES) modelling. If any one of u have work on it plz let me know. I will be very thankful...