boolean logic problem

Discussion in 'Homework Help' started by fran1942, Apr 7, 2013.

  1. fran1942

    Thread Starter Member

    Jul 26, 2010
    58
    0
    Hello, I had to do complete the problems as outlined below this paragraph. I completed parts a-b as per the attached image, however I cannot complete part c which is 'how to use De Morgan's theorem to prove a relationship between the two Karnaugh map simplified formulas'. Can anyone see what I am doing wrong here ?
    Thanks kindly for any help.

    (a)
    Design a circuit which has the four bits of a BCD number as its inputs and
    has an output X so that:
    X = 0 if inputs are a valid BCD number
    X = 1 if inputs are an invalid BCD number.
    (b)
    Redesign the circuit of (a) so that:
    X = 1 for valid BCD
    X = 0 for invalid BCD.
    (Note: DO NOT just invert your input (a).)
    (c)
    Use de Morgan’s theorem to prove that the Boolean Algebra expressions
    you obtained in (a) and (b) are the inverse of each other.




     
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  2. WBahn

    Moderator

    Mar 31, 2012
    17,715
    4,788
    How can we tell what you are doing wrong on Part C when you haven't shown us what you are doing on Part C at all?

    Your Part A and Part B work is fine.

    Post your best effort for Part C so that we have a springboard to work from.
     
  3. djsfantasi

    AAC Fanatic!

    Apr 11, 2010
    2,790
    827
    Hint!

    Rewrite your solutions in parts a and b, to use different variables:

    X=A(B+C)
    Y=A'+B'C'

    Then, to prove part C, you need to show that X and Y' are the same. Using DeMorgan's, this is easy...
     
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