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Practice using K-Maps

  1. Feb 15, 2015 #1

    Zondrina

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

    1. Draw the K-Map for ##F = a \bar b + b \bar c d + cd + \bar a c d + a \bar b \bar c d## and minimize the expression.

    2. Find a simplified expression for the K-map:

    Screen Shot 2015-02-15 at 2.20.14 PM.png

    2. Relevant equations


    3. The attempt at a solution

    My work for each question is shown in the image below. I hope that I have done everything properly:

    IMG_0527.jpg

    If someone could verify my work it would be much appreciated.

    Thank you.
     
  2. jcsd
  3. Feb 16, 2015 #2

    donpacino

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    Why do you have don't cares? either you are not using them correctly, or there is information you are not giving us.
    Also I am fairly certain your kmap is not correct.
     
  4. Feb 16, 2015 #3

    Zondrina

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    The don't cares are given as stated, and the questions are given exactly as I've mentioned in the first post.

    What leads you to believe my K-Map for the first problem is incorrect?
     
  5. Feb 16, 2015 #4

    donpacino

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    ohhh my god, I thought the Kmap show above was the Kmap from the first problem. disregard what I said before...


    For problem #1 I would check your work again
     
  6. Feb 16, 2015 #5

    donpacino

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    for number 2, you can get it simpler. Why are you doing so much algebra. The beauty of the K map allows you to create the logic functions simply.
    I only did one algebra step.
     
  7. Feb 16, 2015 #6

    Zondrina

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    No problem, perhaps it was a little confusing.

    I assume the K-Map for the first problem is wrong because it should look like this:

    e e 1 e
    e 1 1 e
    e 1 1 e
    1 1 1 e

    Where I used e to denote an empty spot on the map.

    For the second question, I can't see how to get it any simpler. I thought the loops I used were as large as possible.
     
  8. Feb 16, 2015 #7

    donpacino

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    your correction to #1 is still not correct. look at your AB' term.

    for the second question I have two comments. You don't need all that algebra. It defeats the purpose of using a kmap. it should be 1, maybe two steps.
    That being said, you have a redundant term in your final answer
     
  9. Feb 16, 2015 #8

    Zondrina

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    Oh whoops, I missed a one on the bottom right corner there, it should be:

    e e 1 e
    e 1 1 e
    e 1 1 e
    1 1 1 1

    Then taking the biggest loops I get ##F = a \bar b + bd + \bar a c d## for the first problem.

    Upon looking at the second problem with a different vision now, I believe It should be:

    $$F = c \bar d + a \bar b + a + \bar a \bar b \bar c \bar d = a + c \bar d + \bar a \bar b \bar c \bar d$$.
     
  10. Feb 16, 2015 #9

    donpacino

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    #1.) Nice job!!

    #2.)that is not correct, i know that because the expression a does not work in this case.
    look at your final answer for #2 in your original work. It is very close to being correct. You can get to that point simply by looking at the loops.
     
  11. Feb 16, 2015 #10

    Zondrina

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    That's weird, thought I had it that time. I see the problem now though, I have an extra loop along the bottom row that's been confusing me.

    So removing that extra loop, I have three loops. The one along the right column, the one along the bottom half of the left column, and the one surrounding the four corners. Reading the loops off I get:

    $$F = c \bar d + a \bar c \bar d + \bar b \bar d = \bar d [ c + a \bar c + \bar b] = \bar d [ a + \bar b + c ]$$
     
    Last edited: Feb 16, 2015
  12. Feb 17, 2015 #11

    donpacino

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    thats what I got.
     
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