BCD Counter

Discussion in 'Homework Help' started by eXodus, Mar 26, 2007.

  1. eXodus

    Thread Starter New Member

    Mar 26, 2007
    1
    0
    I've got most of the formulas worked out, but the Counter still isn't working properly. The ones that I think are wrong are:

    K' = B'C'D'

    I came up with

    K = BCD

    But I am sure that is incorrect. I just don't know what to do with it.

    K' = A'D' + A'C'

    I came up with

    K = (A+D)(A+C)

    Which I figured out after I posted this is correct! Yay for me!

    Everything else I did looks good to me, so if it still doesn't work after some help, I will post more information.

    Thanks in advance to anyone who helps out!
     
  2. thingmaker3

    Retired Moderator

    May 16, 2005
    5,072
    6
    The output is low when all three of the inputs are low. What kind of gate does that?


    Yay indeed! It is correct. But is it simplified? Can you generate K with two gates instead of three by applying one of the Boolean Algebra Laws?
     
  3. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    NOT both sides:

    K'' = (B'C'D')'

    Think of DeMorgan's Theorum: (A.B)' = (A' + B')

    (B'C'D')' = (B'' + C'' + D'')

    B'' = B
    C'' = C
    D'' = D

    And

    K'' = K

    Therefore:

    K' = B'C'D' simplifies to K = B + C + D

    Dave
     
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