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How to identify XOR in K-Maps

  1. Apr 19, 2015 #1

    Zondrina

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    Homework Helper

    1. The problem statement, all variables and given/known data

    Using XK-map techniques, obtain the minimum Boolean expression for the following map:

    Screen Shot 2015-04-19 at 1.58.29 PM.png

    2. Relevant equations


    3. The attempt at a solution

    So I've been doing some reading and I found this has to do with Reed Muller logic. This was unfortunately not covered in the course I'm taking, so I'm a tad bit confused.

    How exactly am I supposed to circle this map? I know I have to circle groups of zeroes and ones such that the parity of the ones is odd and the parity of the zeroes is even.

    For reference, the answer is listed as:

    $$Z = \bar a \bigoplus b \bigoplus c \bigoplus d$$

    I have experimented with a few circling combinations, but cannot find one that gives the answer above.
     
  2. jcsd
  3. Apr 19, 2015 #2

    mfb

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    2016 Award

    Staff: Mentor

    You could "circle" the four "0" for not A i guess. They all have odd parity for B,C,D. Similar for A.
    That does not give nice square blocks - it cannot, you are looking for XOR.
     
  4. Apr 19, 2015 #3

    Zondrina

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    After staring at this for a few more minutes, I came up with this:

    Screen Shot 2015-04-19 at 1.58.29 PM.png

    So the black box would be ##\bar a##. The red box would be ##b##. The blue box would be ##c##. The green box would be ##d##.

    So ##z = \bar a \oplus b \oplus c \oplus d##.
     
    Last edited: Apr 19, 2015
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