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
    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
    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
    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
    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
    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
    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
    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
    SheldonCooper
    Thanks buddy..It's really helpful.
  • haree
    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.

Related Posts

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...
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...
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...
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 ​
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...