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Question on State Table Outputs

Discussion in 'Electronic Basics' started by Steven O., Nov 9, 2004.

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  1. Steven O.

    Steven O. Guest

    Hi. I'm taking a course on introductory digital logic, and there is a
    question where I have a disagreement with the instructor, and I think
    he may be mistaken on a certain point. We are using the text Digital
    Design by Mano, and while the book is generally very good, I think
    even the text is not fully clear on this.

    Suppose you have a State Table for a simple circuit with, say, two
    flip flops (A and B), input X, and output Y. So the headings for the
    table are:

    Present State (time T) Input (T) Next State (T+1) Output (T+1)
    A_______B__________X_______ A____ B_____________ Y

    Now, the question is right there in the table heading, because the
    instructor says that the output column, Y, should be for time T --
    that is, it is based on the states of A and B at time T. To me that
    makes no sense -- it seems the whole point is to start with A and B at
    time T, put in your input X, and see what A, B, and Y are at time T+1.
    So, that's basically the question -- is the output column for time T,
    or for time T+1?

    Thanks in advance for all replies.

    Steve O.



    "Spying On The College Of Your Choice" -- How to pick the college that is the Best Match for a high school student's needs.
    www.SpyingOnTheCollegeOfYourChoice.com
     
  2. Tim Wescott

    Tim Wescott Guest

    Well, the first thing to remember with any kind of a paper method like
    this is that it means whatever the hell you want it to mean; as long as
    you are clear and unambiguous about it then you're fine.

    Second, there are generally two types of state machines, whose names I
    cannot remember (one is Mealy, I think, but I'm just an analog guy who
    writes software). One type has outputs which are entirely dependent on
    the state, and the other has outputs that are a function of the state
    and the input. In the case of the second type I would be less confused
    by a table that shows the _current_ output as a function of the
    _current_ state and _current_ input -- particularly if there were
    (shudder) input changes going on in between state transitions. Even for
    the first type, knowing the _current_ output given the _current_ state
    would, I think, be least confusing for me.

    My suggestion would be to go ahead and use the notation as used in the
    class, and make sure that you're facile with it. As soon as you're out
    of that class you can do whatever the heck you want -- your reader's
    questions will give you guidance about whether you made the best choice.
     
  3. Devices with memory produce outputs at time T+1 based on the outputs
    and inputs at time T. The outputs are locally stored inputs.
     
  4. Andrew Holme

    Andrew Holme Guest

    If Y is a combinatorial logic function of A and B _only_, then it doesn't
    matter whether you tabulate Y(T) or Y(T+1) as long as you say which it is.
    You've got A(T), B(T), A(T+1) and B(T+1) all tabulated on the same line.

    Y(T) = f( A(T), B(T) )
    Y(T+1) = f( A(T+1), B(T+1) )

    i.e. Y(n) = f (A(n), B(n))
     
  5. Steven O.

    Steven O. Guest

    I thought it was implied that since we have flip-flops, the logic is
    sequential and not combinatorial. But if I make that explicit -- this
    is sequential logic -- then how does the answer to my question come
    out?



    "Spying On The College Of Your Choice" -- How to pick the college that is the Best Match for a high school student's needs.
    www.SpyingOnTheCollegeOfYourChoice.com
     
  6. There are two major state machine types : Moore and Mealy.

    Moore : output is only dependent on the current state

    Mealy : output is a combinatorial function of current state and
    current input(s)

    So, for your example, Output column should be for time (T), not (T+1).
    You may take a look at Randy H Katz Contemporary Logic Design book
    from '93, available online at
    http://www2.ele.ufes.br/~ailson/digital2/cld/CLD.html, chapter 8 :
    Finite state machine design.


    Have fun!

    Francois Choquette
     
  7. Andrew Holme

    Andrew Holme Guest

    State machines contain combinatorial logic and flip-flops. The sum of
    the parts is sequential logic.
     
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