BCD Counter

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

  1. eXodus

    Thread Starter New Member

    Mar 26, 2007
    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
    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
    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


    K'' = K


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