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Math Help - Karnaugh Maps

  1. #1
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    Karnaugh Maps

    Hello,

    Given the following:
    r = x' y' z' + (xy)' + x z' + x' y z'

    (a) Draw the Karnaugh map
    (b) From the Karnaugh map, find the minimized DNF
    (c) Draw the logical circuit corresponding to this minimised DNF.

    ************************************************** *********
    Work so far.

    (a)What throws me off is the (xy)' part. Using De Morgan's laws, can this be equated to x' + y'. If so, can I write r as:
    r = x' y' z' + x' + y' + x z' + x' y z'

    Assuming that r can be rewritten as shown above, r = x' y' z' + x' + y' + x z' + x' y z', is this a correct representation of the Karnaugh map:
    y' y y y'
    x' 1 1 1 1
    x 1 1 0 1
    z' z' z z

    (b) The minimised DNF would then be: x' + y' + z' (from circles in Karnaugh map).

    (c) A logic circuit could then be constructed in the following way:
    Karnaugh Maps-logiccircuit.jpg

    I would really appreciate an indication on whether or not I am interpreting this right. Thank you in advance.
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: Karnaugh Maps

    Hi aprilrocks92!

    You are right!
    Thanks from aprilrocks92
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