Validity of equation

Discussion in 'Electronics Homework Help' started by anacondaonline, May 13, 2018.

  1. anacondaonline

    anacondaonline

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    I'm trying to solve this question from my book.

    [​IMG]




    Book has given this solution :

    [​IMG]


    I don't understand that red marked part in the given solution.

    Do you think book solution is correct? Could you please explain that red marked part. how did the book arrive to that from the earlier step? I'm stuck right at that part.

    Need help.
     
    anacondaonline, May 13, 2018
    #1
  2. anacondaonline

    anacondaonline

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    I have understood the above part. ..... book is using "*" definition there.

    But I'm stuck in the next step. Is it a law ? which law ? Please see below
    [​IMG]
     
    anacondaonline, May 13, 2018
    #2
  3. anacondaonline

    Laplace

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    Have you tried multiple application of DeMorgan's law?
     
    Laplace, May 14, 2018
    #3
  4. anacondaonline

    Ratch

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    The book solution is correct, but the solution method is in error. They made a mistake at the place you cannot understand. The whole expression should be have a bar over it. They must have made another mistake later to get the correct answer. Two wrongs make it right.

    Since the "*" means Exclusive OR, why not rewrite the equation as B(AB'+A'B)'+B'(AB'+A'B) and solve that instead?

    I am enclosing a program I wrote some years ago to give the minterms of a logical expression.

    Ratch
     

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    Ratch, May 14, 2018
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  5. anacondaonline

    Ratch

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    The book is correct here. It is a simple application of DeMorgan's Theorem.

    Ratch
     
    Ratch, May 14, 2018
    #5
  6. anacondaonline

    Harald Kapp Moderator Moderator

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    I don't think so. The "*" in the task description is not the usual AND function. "*" is defined as A*B = AB + /A/B instead.
    Assuming that AB means logical AND and "+" means logical OR, then "*" represents an Exclusive NOR.
     
    Harald Kapp, May 15, 2018
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  7. anacondaonline

    Ratch

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    Did I not say in post #4 that the asterisk in that problem means XOR? I stand by my statement that the solution is correct, but the method contains an error.

    Ratch
     
    Ratch, May 15, 2018
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  8. anacondaonline

    Harald Kapp Moderator Moderator

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    I'm sorry, I missed that part. It's still XNOR, however.
     
    Harald Kapp, May 15, 2018
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  9. anacondaonline

    Laplace

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    The original question was how did the author arrive at the circled expression? It was done by multiple application of DeMorgan's Theorem, {When breaking an overbar, the operation enclosed by the overbar changes between AND / OR}.
    Screenshot from 2018-05-15 10-46-37.png
     
    Laplace, May 15, 2018
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  10. anacondaonline

    Ratch

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    Too much time has been spent on this problem already. DeMorgan's theorem is unnecessary.

    B*A*B
    B*(A*B)
    B(A*B)'+B'(A*B)
    B(AB+A'B')+B'(AB'+A'B)
    ABB+A'B'B+AB'B'+A'BB'
    AB +0 +AB' +0
    A(B+B')
    A

    Ratch
     
    Ratch, May 15, 2018
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  11. anacondaonline

    Ratch

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    DeMorgan's theorem is not necessary.

    (A'B'+AB)'
    1-(A'B'+AB) ; Complement of (A'B'+AB)
    (A'B'+A'B+AB'+AB) - (A'B'+AB) ; 1 = (A'B'+A'B+AB'+AB)
    A'B+AB'

    Ratch
     
    Ratch, May 16, 2018
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  12. anacondaonline

    Laplace

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    True; however, they do teach DeMorgan's Theorem for a reason. But one thing I was never taught is the use of the Boolean minus "-" operation. There is the AND gate, the OR gate, the NOT gate. Where does one get a MINUS gate?
     
    Laplace, May 16, 2018
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  13. anacondaonline

    Ratch

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    It is not a gate, it is an operation, like add or multiply. To complement any Boolean term or expression, just subtract it from "1". Just like you would complement a decimal number by subtracting it from "10". It corresponds to a K-map with the unmarked squares taken as the complement.

    Ratch
     
    Ratch, May 16, 2018
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  14. anacondaonline

    Laplace

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    So you are offering a K-map as the solution to a Boolean equation. When has that ever been considered rigorous?
     
    Laplace, May 16, 2018
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  15. anacondaonline

    Ratch

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    I am using the K-map as an explanation of why the subtraction of a Boolean term from "1" gives the complement of the term. The K-map is as rigorous as a slide rule is for what it does.

    Ratch
     
    Ratch, May 16, 2018
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