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  • nareshkumar6539

    Member • 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.
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  • SheldonCooper

    Member • 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.
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  • nareshkumar6539

    Member • 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
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  • SheldonCooper

    Member • 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.
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  • SheldonCooper

    Member • 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.
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  • nareshkumar6539

    Member • 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]
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  • nareshkumar6539

    Member • 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
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  • SheldonCooper

    Member • Nov 28, 2011

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

    Member • 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.
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