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Basic Logic Gates / Pulse Train Problem (Includes Solution)

  1. Feb 9, 2013 #1

    s3a

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    1. The problem statement, all variables and given/known data
    The problem and its solution are attached.

    2. Relevant equations
    N/A

    3. The attempt at a solution
    I'm very confused about how output pulse trains work. I already checked online (including Wikipedia) so, could someone please give me an explanation of the absolute basics in an easy-to-understand way?

    I'm confused about what the “rectangle-ness” around the numbers is for and how it works.

    What I DO get is that the output is the same as the input A since input B is a constant 1 and, converting “1” to “True”, we get unknown AND True = unknown.

    Any input for helping me fully understand this problem would be greatly appreciated!
     

    Attached Files:

  2. jcsd
  3. Feb 9, 2013 #2

    mfb

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    That is just a graphical representation of the input - the line is high for 1 and low for 0.
     
  4. Feb 9, 2013 #3

    s3a

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    Oh but, how do I know what A (and, by consequence, Y) is equal to?

    In other words, what is the computational step (no matter how simple it may be)?
     
  5. Feb 9, 2013 #4

    mfb

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    That is given there. Input A starts with a 1 (written above "a"), this is followed by a 0 ("b"), ...
    Well, it could start with "h" as well, but that changes nothing.
     
  6. Feb 9, 2013 #5

    s3a

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    So, A is a sequence of digits rather than one final answer?

    I was thinking it would be (a OR b OR c OR d OR e OR f OR g OR h) = (0 or 1) = A or something like that. (By a capital "OR", I am referring to boolean logic whereas with the lowercase "or", I am just stating that the final value of A is either a 0 or a 1.)

    I'm still confused. (Sorry.)
     
  7. Feb 9, 2013 #6

    mfb

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    A pulse train, right (where the individual bits are "wagons").
     
  8. Feb 9, 2013 #7

    s3a

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    1) Is the "rectangle-ness" part of the value A or is it just a fancy graphical drawing to what A really is which is only the individual digits (=wagons, as you mentioned in your last post)?

    2) Is Y = {(a AND B),(b AND B),(c AND B),(d AND B),(e AND B),(f AND B),(g AND B),(h AND B)} = {(1 AND 1),(0 AND 1),(0 AND 1),(1 AND 1),(1 AND 1),(0 AND 1),(1 AND 1),(0 AND 1)}

    3) Is a pulse train a SET of values (in the mathematical sense)?
     
  9. Feb 9, 2013 #8

    mfb

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    It is the same as the written "0" and "1" - just another way to graph them.

    A sequence of values, they have some order.
     
  10. Feb 9, 2013 #9

    s3a

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    I think I get it now (thanks to what you said combined with looking at problems later in the book where B is not a constant 1 and applying what I now know).

    Thanks. :)
     
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