Boolean function simplification and implementation, MMExer3.19a

Discussion in 'Homework Help' started by PG1995, Dec 9, 2011.

  1. PG1995

    Thread Starter Active Member

    Apr 15, 2011
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    Hi

    Please have a look here to see my question. The solution is here. Please help me. Thanks a lot.

    Regards
    PG
     
  2. Georacer

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    Nov 25, 2009
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    I think I answered that question in this post (http://forum.allaboutcircuits.com/showthread.php?t=63147).

    Generally, I find those "solutions" you have found rather unprofessional. Are they from a book of yours or from some slides your professor has given you? I suggest you stick to what you "feel" that is correct, and not to what you are told is correct.
    Personally, I will stick to what I 'm posting, until I 'm challenged by someone proving me wrong.
     
  3. PG1995

    Thread Starter Active Member

    Apr 15, 2011
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    Thank you.

    That was a different problem.

    The solutions are from 'professional' solution manual published Pearson Education for the book Digital Design by Morris Mano.

    Best regards
    PG
     
  4. Georacer

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    Nov 25, 2009
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    Which edition of the book are the solutions from? Generally the Morris Mano book is very high quality. Most of my digital knowledge comes from this book actually.

    In the other thread I linked to, I gave you the method of extracting the NAND and NOR circuits from boolean expressions. Was it too complex? Do you want me to break it down more?

    Give it a try for this and the other problem and post your work.
     
    PG1995 likes this.
  5. PG1995

    Thread Starter Active Member

    Apr 15, 2011
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    Hi GeoRacer

    It's 4th Ed. Have you used Digital Fundamentals by Floyd. I find Floyd's book more straightforward. In the past I have shunned the Morris Mano's as much as I can. But if you say, it's a good one, I would give it a try. :)

    No, sorry. You see, I checked your reply to the other linked thread after I had posted this thread. You have given a general method there. I will read it thoroughly and then ask you any question if there is one. Many thanks.

    Best regards
    PG
     
  6. Georacer

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    Nov 25, 2009
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    Never read Floyd. Probably never will, but I might check on it if I 'm too curious. Don't feel constrained by one tutoring source. What doesn't work for one man may do wonders to another.
     
  7. PG1995

    Thread Starter Active Member

    Apr 15, 2011
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    Hi

    Please have a look on the attachment and let me know if my solution is correct. Thank you.

    Regards
    PG
     
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  8. Georacer

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    Nov 25, 2009
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    What method did you use to get to your result? I don't see any reasoning to it.

    There are several mistakes in your solution.
    First of all, the expression (Y')(X'+Z')(W+X') isn't a valid expression for F. Take for example the input WXYZ=0100 gives a result of (0')(1'+0')(0+1')=1(0+1)(0+0)=0=FALSE, where, based on the K-map we should have a F(0100)=TRUE.

    Please be more methodical in your solutions.

    Take another read here:
    What this says is that you find the minimal SoP expression for the F' expression and then negate it to find the NOR circuit.

    Let's do this one together, using your K-map:
    F'=w'z+xz+wxy
    Now we negate the expression to get
    F=(F')'
    =(w'z+xz+wxy)'
    =(w'z)'(xz)'(wxy)'
    =(w+z')(x'+z')(w'+x'+y')
    and then
    F=((F)')'
    =(((w+z')(x'+z')(w'+x'+y'))')'
    =((w+z')'+(x'+z')'+(w'+x'+y')')'
    =NOR( NOR(w,z') , NOR(x',z') , NOR(w',x',y'))

    It's tedious, but at least I, don't know any other algorithmic way.

    The other issue about your effort I 'd like to address, is that you couldn't replicate the expression F=y'(x'+z')(w+x') in a circuit.

    The circuit you posted is for the expression ((x'+z')'+(x'+w)'+y')'. That is because the last gate on the right is a NOR one, not an AND.

    Can you work the same results as me and post a correct circuit? I 'll search for some gate resources if you have trouble with them.
     
  9. Georacer

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    Nov 25, 2009
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    I 'd also like to remind you that:
    [​IMG]
    (Image created by Bill_Marsden)
     
  10. PG1995

    Thread Starter Active Member

    Apr 15, 2011
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    Thanks a lot, GeoRacer, for the reply.

    Please have a look on the attachment and please let me know what you think. Once again, many thanks. It seems your method is more general but the that method also works for two-level implementation. The book also says for two-level NAND implementation you need to have circuit in SOP form.

    Best regards
    PG
     
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    Last edited: Dec 9, 2011
  11. Georacer

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