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Homework Help: Finding the complement using demorgans and involution (boolean alg)

  1. Sep 5, 2013 #1
    1. The problem statement, all variables and given/known data
    Use only DeMorgan's relationships and Involution to find the complements of the following functions:
    a.) f(A,B,C,D) = [A+(BCD)'][(AD)'+B(C'+A)]

    2. Relevant equations
    Demorgans (x1 + x2 + ... + xn)' = x1'x2'...xn'

    Involution (x')' = x

    3. The attempt at a solution

    [[A+(BCD)'][(AD)'+B(C'+A)]]' to find the compliment, then using demorgans
    [A+(BCD)']' + [(AD)'+B(C'+A)]'
    [A'(BCD)] + (AD)[B(C'+A)]'
    A'BCD + (AD)[B' + (C'+A)']
    A'BCD + (AD)(B' + CA')

    from here I don't know where to go, i would think the right side of the equation could turn to ADB' + ADCA' but i'm not sure, if it can ADCA' would just be 0 since AA' = 0. Don't know if I can do that though, just looking for some input and hopefully I didn't make a mistake towards the begining.
    Last edited: Sep 6, 2013
  2. jcsd
  3. Sep 6, 2013 #2


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    Staff: Mentor

    Hi buddyblakester, http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif [Broken]

    That is not a correct expression for De Morgan's theorem.
    Last edited by a moderator: May 6, 2017
  4. Sep 6, 2013 #3
    had it on my paper right but yea typed it in wrong, thanks
  5. Sep 7, 2013 #4


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    Staff: Mentor

    I hadn't noticed it was just a typo.

    Yes, that looks right.

    You can check by constructing a Truth Table for the original expression and for your answer.
  6. Sep 9, 2013 #5
    ok cool, seems like AA' = 0 and A + A' = 1 can really reduce some of these kinds of equations in my homework. thanks for the feedback
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