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Math Help - boolean logic diagramn

  1. #1
    Member
    Joined
    Nov 2010
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    93

    boolean logic diagramn

    Hello I cannot figure out how the path that I have labelled with the arrow works.
    Apparently it is feeding the output back into the input, but how can you generate this output before your input is known ?

    Can someone please help me understand how this works and how you would draw up a truth table to express it.

    Here is the image link:
    http://bphprint.co.nz/circ.jpg

    Thanks kindly for any help.
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  2. #2
    Member
    Joined
    May 2011
    From
    Sacramento, CA
    Posts
    165
    If I understand the gates (i.e., A connected to an OR-gate and B connected to an AND-gate) and connections correctly, we might express it as a statement:

    Q = min(max(A, X), B')

    Where B' = 1-B, X is unknown, and true inputs are 1, false inputs 0. There are four possible cases.

    Spoiler:
    Let A = B = 0 (B' = 1).
    Q = min(max(0, X), 1)
    Q = X

    Let A = B = 1 (B' = 0)
    Q = min(max(1, X), 0)
    Q = 0

    Let A = 0, B = 1 (B' = 0)
    Q = min(max(0, X), 0)
    Q = 0

    Let A = 1, B = 0, (B' = 1)
    Q = min(max(1, X), 1)
    Q = 1


    In three of the cases the output is wholly determined by the values of A and B, regardless of what X is. The one case that is mysterious is whenever A and B are both false. But if I think of this in terms of electric circuits, then if both A and B have no current, then there is no possible way for X to have current. Therefore, we can just define X = 0 there. I don't know if that is the current assessment, but I find that diagram a bit odd. These were my thoughts on it.

    I noticed a second thought just now. By what I said above, X = A will produce the same results. Redefine the diagram in those terms and see what you think.
    Last edited by bryangoodrich; May 30th 2011 at 01:13 AM. Reason: A second thought
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