K-map Paradox?

Discussion in 'Homework Help' started by Nerfhurter, Dec 10, 2010.

  1. Nerfhurter

    Thread Starter New Member

    Dec 10, 2010
    9
    0
    Hello, I'm fairly new to electrical engineering, in my class we are working with 7 segment display (common anode).
    I've come up with the following k-map truth table for "D" input (~ is NOT).
    ~Z Z
    ~X~Y 0 0
    ~X Y 1 1
    X Y 1 0
    X~Y 1 1

    I used k-maps to get the following simplified expression Hi=~XY+X~Z+X~Y. For the third term I use an invert after ~XY, but that makes one expression ORd with its inverse. This is giving, as expected 1's for all possible inputs since I have one term ORd with its inverse all possible inputs give a 1. I'm wondering where I went wrong, any help is much appreciated.
     
  2. StayatHomeElectronics

    Well-Known Member

    Sep 25, 2008
    864
    40
    I am a little confused at what simplification you are actually doing.

    Are you saying that ~XY = ~(X~Y)?? This is not true. Try making a truth table for each of the terms in question...
     
  3. Nerfhurter

    Thread Starter New Member

    Dec 10, 2010
    9
    0
    Yes, okay I think I got it but why is ~xy not equal to ~(x~y)?
     
  4. StayatHomeElectronics

    Well-Known Member

    Sep 25, 2008
    864
    40
    Try drawing out the truth table for each:

    X Y ~XY X~Y
    0 0....0....0
    0 1....1....0
    1 0....0....1
    1 1....0....0

    Inverting one will definitely not give you the other.
     
  5. Nerfhurter

    Thread Starter New Member

    Dec 10, 2010
    9
    0
    Oh, thanks so you can't invert K-maps becuase they are outputs?
    If F1=AB then F1^-1 =/= (AB)^-1.
     
  6. StayatHomeElectronics

    Well-Known Member

    Sep 25, 2008
    864
    40
    If F1 = AB, then F1^-1 = (AB)^-1 =/= (A^-1B^-1). You have to be very precise with the math...
     
  7. Nerfhurter

    Thread Starter New Member

    Dec 10, 2010
    9
    0
    So in terms of circuit design, if I have XnotY in a circuit and I want notXY, I know I can't invert XnotY but is there something I can do to reduce amount of gates, or do I just make another "branch" with notXY?
     
  8. StayatHomeElectronics

    Well-Known Member

    Sep 25, 2008
    864
    40
    If you use the example that you have given above, there is nothing that you can do to reduce the circuit further. You must add another branch.
     
  9. Nerfhurter

    Thread Starter New Member

    Dec 10, 2010
    9
    0
    OK, thanks a lot for all your help.
     
Loading...