Help with implement NAND circuit

Discussion in 'Homework Help' started by mwl, Oct 12, 2011.

  1. mwl

    Thread Starter New Member

    Sep 28, 2011
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    Hello dear members of AAC! :)

    I'm having problem with implement this circuit with ONLY 2 input - NAND ports:

    F = ACD + AB + BC'

    Also, I don't know if I can minize it. I tried, but I were stuck in the same point =//
     
    Last edited: Oct 12, 2011
  2. Georacer

    Moderator

    Nov 25, 2009
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    Can you post your efforts, for us to see and comment on?
     
  3. mwl

    Thread Starter New Member

    Sep 28, 2011
    7
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    Course!
    Well, I tried to manualy minize it, but all i got was:

    F = A(CD + B) + BC'

    And that's all!

    I'm really confused about the De Morgan's theorem, how to use it to design and draw a circuit only with the NAND ports. I know how to make an inversor, AND and OR ports from only NANDs, but I'm not sure if that is all that I need for this.

    Also, I used a software called "Logic Friday" to minimize it, but it gave me the same logical function.
     
  4. panic mode

    Senior Member

    Oct 10, 2011
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    that is already minimized form
    to make use of NANDs means to produce terms in form

    (XY)'

    in your case it would be something like

    ACD+AB+BC'=
    (ACD+AB+BC')"=
    [((ACD)'(AB)'(BC')']'=
    [((AC)"D)'(AB)'(BC')']'
    etc.

    note that (AC)' need to be inverted one more time before anding with D.

    we can do the same to get around 2-input limitations for final gate. in example here that one is still using 3 inputs but you can finish it same way the rest was done (hint, read the note).
     
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  5. mwl

    Thread Starter New Member

    Sep 28, 2011
    7
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    Thanks a lot for the answer!

    From what I saw, you did this:

    = (ACD+AB+BC')" First, you double negated all the equation
    = [((ACD)'(AB)'(BC')']' After, used De Morgan,
    [((AC)"D)'(AB)'(BC')']' And lastly, i didn't understand how you isolated AC from D.
     
  6. Georacer

    Moderator

    Nov 25, 2009
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    It's nothing really: ACD=(AC)D=(AC)''D
    because F=F''
     
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  7. mwl

    Thread Starter New Member

    Sep 28, 2011
    7
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    Thanks a lot again! ;)
    AAC > all!
     
  8. mwl

    Thread Starter New Member

    Sep 28, 2011
    7
    0
    Also, if I can have another answer =)

    I just put this equation into some map minimizer.


    Entered:
    F=x + x'z + x'w + z'w

    And i got this:

    Minimized:
    F = x + z + w

    Someone how what simplification should I do here?
     
  9. Georacer

    Moderator

    Nov 25, 2009
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    Are you asking how the software got the final expression or how to implement F=x+z+w with a NAND gate?

    If it's the latter, try to think of it like this: F=x+z+w=(x'z'w')'
    and also: a NAND b NAND c = (a NAND b) NAND c.

    Can you figure anything out?
     
  10. mwl

    Thread Starter New Member

    Sep 28, 2011
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    Sorry! I wasnt clear!
    What I wanted to know is how the software got the final expression :)
     
  11. Georacer

    Moderator

    Nov 25, 2009
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    The software might have used a myriad of methods.

    The most brain-dead and fool-proof (but not the shortest) method you can use, is to construct a truth table from the given expression and then find the Sum of Products solution, which is most of the time, the shortest.
     
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