Boolean expression using NANDS

Discussion in 'Homework Help' started by yagmai, Aug 27, 2005.

  1. yagmai

    Thread Starter New Member

    May 19, 2005
    hi guys,
    I have

    X = A'B + CD + AD'

    I need to implement X using 2 inputs NAND Gates

    This is wat I get

    ((A'B)' (CD)' (AD'))'

    However as u can c, there is a need to use 3 inputs NAND gate. How to further simplify it?? Thanks
  2. techduq

    New Member

    Aug 31, 2005

    Is there a limit on how many NANDs you may use? I have a solution that uses 8 2-input NANDs. 3 of those are simply NAND-connected inverters (i.e., a NAND with both inputs shorted to mimic an inverter).

    You'll find that the easiest way to do problems like this is to use "graphical DeMorganizing" (that's my term, I don't know what others call it). To quickly DeMorganize with this method, you change the basic gate from AND to OR or OR to AND, depending on what you have, and you invert the bubble status- that is, wherever you have bubbles, omit them, and where you don't have them, put them in. For example, an AND becomes an OR with bubbles added to all inputs and the output. This allows "cancelling" of bubbles in series, and certain other reductions/simplifications. Give it a try, it's not hard. Good luck!
  3. dragan733

    Senior Member

    Dec 12, 2004
    Here is the result:
  4. aibelectronics


    Aug 26, 2005
    CUTE schematic! What editor did you use?