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Thread: Boolean algebra

  1. #1 Boolean algebra 
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    b) Find a Boolean expression C, depending on the Boolean variables A, B, such that the following truth table is correct.

    A B C
    0 0 1
    0 1 0
    1 0 1
    1 1 0


    Can anyone show me a technique to find easily boolean expressions of this kind?


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  3. #2  
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    NOT B

    To me it simply comes with practice, look for similarities, in this case C is related to B. In fact it is so simple I reckon you might have copied it down wrong, please check.


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  4. #3  
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    yes the answer is NOT B can u please show me the workign how u arrive to not b?
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  5. #4  
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    I simply compared it with A and then B. Since I do not know how the brain works I simply cannot provide anymore information than that. I spotted a pattern, had it been a more complicated set I might have used a Venn diagram or drawn a set of truth tables but I noticed the answer before I had time to consider these options.
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  6. #5  
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    Well there aren't that many options, right? AND XOR OR NOT. Just brute force check all of them and see if any of them are the right answer.
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    Quote Originally Posted by Numsgil
    Well there aren't that many options, right? AND XOR OR NOT. Just brute force check all of them and see if any of them are the right answer.

    so what about....

    ABC D
    000=0
    001=0
    010=0
    011=1
    100=1
    101=0
    110=0
    111=0

    Here's the solution...
    Take the 1's in line D as there are only 2 of them


    Line 4 D = ( /A & B & C)
    LIne 5 D = (A & /B &/C

    Now just OR them such that

    D = (/A & B & C) + (A &/B & /C)
    Where '/' = NOT, '+' = OR and '&' = AND.

    Sometimes the result above can be simplified, but I can't remember the name of the law(s) - this 73yr old brain seems to have forgotton it! Some how De'Moire rings a bell but Moire I remember is an optical effect - anybody?
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  8. #7  
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    i liked the last one but the fact is that i have 2 variables and not three to get D, is that right?

    Let me know why u add D, when it is asking to find C, or prove the true of C

    C=NOT B is the answer but i want to understand the technique of finding these values,..


    why u take the 4D and the 5D how u get 1 there?
    Can u explain this as well?




    Thanks

    Anto
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    I was replying to nusmgil ie to show them that their answer was technically incorrect, I also thought you might like to see the solution to a more difficult one, if you wish to remove 'D' just remove all references to 'C' then rename all references to 'D' as 'C' - it's that simple.

    ie LIne 5 D = A & /B &/C

    would then become C = A & /B

    Keep reading through what I have written and practice it.

    ABC D
    000=0 this is line 1
    001=0 this is line 2
    010=0 this is line 3
    011=1 this is line 4
    100=1 this is line 5 ( in line 5 D = 1 (ie column D))
    101=0
    110=0
    111=0

    OK?
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  10. #9  
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    sorry this is even more confusing now....
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  11. #10  
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    Hmmm,
    Perhaps you could tell us what you do understand, ie how far you have got with this,
    be honest and tell us where the question comes from (homework?) then maybe we can work to improve your knowledge.
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  12. #11  
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    actually is my test tomorrow in computer science, and this may be part of it.

    what i do understand is
    i.e

    A B C
    0 0 0
    0 0 1
    0 1 0
    0 1 1
    1 0 0
    1 0 1
    1 1 0
    1 1 1 2X2X2X2=16 COMBINATIONS, i know where this is coming from but what i want to know how to use them, so if u can give an explanation it will be great, with the question above,...
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  13. #12  
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    If you are going to leave it to the day before your exam then you will probably fail, and for good reason - you have not studied. I have given you a basic outline of what you asked for in your first post, I have shown you how to construct the Boolean equations for each line and then combine them - at this stage you should understand what I have said, if not then I really don't think anybody can help you in such a short time.


    My advice would be to either study hard at each lesson or learn the phrase "Would like fries with your order sir?".
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  14. #13  
    Forum Masters Degree Numsgil's Avatar
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    Iff there is A and B, and the result is C, there aren't that many combinations. Yes, it gets more complicated with more than two operands, but for two it isn't that bad, because if you try and build up a large chain of operations it ends up just simplifying down. Like !A and !B is the same as !(A or B), etc.

    You must have a textbook or something. Find the chapter on booleans and cram as much of it as possible into your mind for the test as possible. If you do it smartly you should be able to get a significant portion of the test correct.
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  15. #14  
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    Quote Originally Posted by Megabrain
    If you are going to leave it to the day before your exam then you will probably fail, and for good reason - you have not studied. I have given you a basic outline of what you asked for in your first post, I have shown you how to construct the Boolean equations for each line and then combine them - at this stage you should understand what I have said, if not then I really don't think anybody can help you in such a short time.


    My advice would be to either study hard at each lesson or learn the phrase "Would like fries with your order sir?".
    Hostile and not helpful to the OP. If you can't say anything nice...
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  16. #15  
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    Quote Originally Posted by Numsgil
    Well there aren't that many options, right? AND XOR OR NOT. Just brute force check all of them and see if any of them are the right answer.

    Hostile and not helpful to the OP. If you can't say anything nice...


    I seem to remember explaining the process step by step only to find out it's the day before the exam and he wants more than a method he wants the whole answer - it's homework - I pointed out the truth, if he does not study he will fail and end up selling Crusty-Burgers.
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  17. #16  
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    first of all i will not fail, and second i ask for more to gain as much as it is possible before the exam, in my text book is not written that i can use a venn diagram to solve these problems with booleans and when i realized that it is possible and it can solve any problem in computer science i was quite excited and wanted to know more. I don't think that is a bad thing, and i'm not of those who were not studing and selling burgers to fatties. Take a nap.
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  18. #17 Boolean Algebra 
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    This is quite strange, because you didn't specify any operator to be used.
    To deal with it formally, use a K-MAP (Karnaugh Map)
    It's not easy to describe how to use a K-Map, so kindly research about it. You can find it under topics such as Digital Electronics, Digital Design, and even Discrete Mathematics.

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