Help understanding operators and implementation

Discussion in 'Homework Help' started by Damp48, Jun 8, 2011.

  1. Damp48

    Thread Starter New Member

    Jun 8, 2011
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    hi this is my first post here, i've been lurking for a few months. I need help with a logic implementation

    The problem says to find the non-standard form with the minimal number of operators fuction is:

    F = x'zw+xz'w+z'y'z'w'+xy'zw

    I used a kmap to see how it would look, but noticed there are 2 ways of doing it i believe, if the function could be different but with this function. I got :

    F = xw(z'+y')+X'(zw+y'z'w')

    this is the right answer from a solution i have BUT i fail to see how it becomes 9 operators.

    WHen i count these i get 3 OR's, 4 AND's, 6 NOT's. I know i am doing something wrong but my book does not explain any further when it comes to figuring out how many operators. I tried doing the implementations but do not see how they get 9 operators.

    See the attachments.
     
  2. Georacer

    Moderator

    Nov 25, 2009
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    You must first have in mind some implementation hints:
    F=xw(z'+y')+x'(zw+y'z'w')
    =xw(zy)'+x'(zw+(y+z+w)')

    We are thus using one NAND gate ((zy)') and one NOR gate ((y+z+w)') to reduce the NOT gates. In total we have:
    1 NOT
    2 2-input AND
    1 3-input AND
    1 2-input NAND
    1 3-input NOR
    2 2-input OR
    SUM=8 gates

    So, um... yes... 8 gates. Why not?

    But this is not the best solution by a long shot, because those gates come in IC's in packs of 4 or 3. If you use one 3-input AND, you must bring another two along, so you are better off with more gates but of the same type.
     
  3. Damp48

    Thread Starter New Member

    Jun 8, 2011
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    ohh wow thank you so much. I see its with de morgan's theorem that should have been obvious, I've been breaking my head with this all day. It all makes sense now. Thank you.
     
  4. Damp48

    Thread Starter New Member

    Jun 8, 2011
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    i think the schematic looks like this:
     
  5. Damp48

    Thread Starter New Member

    Jun 8, 2011
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    sorry i just realized they actually want 9 operators. currently trying to find how to get it there.
     
  6. Georacer

    Moderator

    Nov 25, 2009
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    I noticed that you wanted 9 operators, but I though a better solution would be more acceptable.
    There's no reason you would want to do it with 9, apart from some professor's inexplicable fixations.

    You can always separate the 3-input AND to get the result you want. Can you guess what will you break it into?
     
  7. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    This might be a solution ....
     
  8. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    It may well be the case that the function

    F = x'zw+xz'w+z'y'z'w'+xy'zw

    cannot be minimised further than

    F=wx'z+wxz'+w'y'z'+wy'z

    for the SOP form.

    I'd be interested to find out.
     
  9. jegues

    Well-Known Member

    Sep 13, 2010
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    My Karnaugh Map draws the same conclusion.
     
  10. Georacer

    Moderator

    Nov 25, 2009
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    This SOP form needs 4 NOT gates and 5 3-input NAND gates to be implemented. 9 gates in 3 IC's in total.

    The solution I suggested in post #2 needs 8 gates but 6 IC's.

    Guess which is better?
     
  11. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    Hi Georacer,

    Did you check that the original

    F = x'zw+xz'w+z'y'z'w'+xy'zw posted by Damp48

    and the subsequent

    F=xw(z'+y')+x'(zw+y'z'w') you posted [as per Damp48's reduction]

    are logically equivalent?

    I'm not sure they are.
     
  12. Georacer

    Moderator

    Nov 25, 2009
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    Blimey, when will I learn?

    Ok, OP, please tell us whether the solution of your book is wrong or you did a typo.
     
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