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Boolean help

  1. Oct 19, 2006 #1
    Can someone help me with this problem.
     

    Attached Files:

  2. jcsd
  3. Oct 19, 2006 #2
    i wanted to proof that that boolean is true. thank you

    i wanted to proof that that boolean is true. thank you
     
  4. Oct 19, 2006 #3
    I need to simplify the following expressions in XOR The simplified answer is only one variable or its complement
     
  5. Oct 20, 2006 #4

    CRGreathouse

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    I can't see the JPEG yet. Why don't you explain the problem and what you've done so far?
     
  6. Oct 20, 2006 #5

    0rthodontist

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    You could use the definition of XOR in terms of and and or. Or you could work directly in terms of XOR. Some properties of XOR can be found here:
    http://en.wikipedia.org/wiki/XOR#Properties
     
    Last edited: Oct 20, 2006
  7. Oct 20, 2006 #6
    One alternative - you can generate a truth table of the expression and see from the table what it is done, but I doubt that any Math teacher would like that, anyway

    For example a
    I belive that you can rearrange the terms and you can simplify them

    e.g.

    A'B XOR BC XOR AB XOR B'C'

    becomes

    A'B XOR AB XOR BC XOR B'C'

    note:
    A'B XOR AB - what does that tell you?

    you can simplyfiy this to get just one variable

    then take BC XOR B'C'

    how can you get a more simple equivalent of this of a form Y XOR Z where Y and Z represent one variable e.g. B or C'.

    When you have this done you should see the answer.

    Example b is a tautology.
     
  8. Oct 21, 2006 #7
    A'b Xor Ab = B?
     
  9. Oct 21, 2006 #8
    Bc Xor B'c'
    =(b Xor C)'
    =b+c'
    =b' Xor C = Bc + B'c'
    = B=c?

    So The Answer Would Be B Xor (b = C) = 0??
     
  10. Oct 21, 2006 #9
    B Xor (b Ξ C)
     
  11. Oct 21, 2006 #10
    TO approve this other problem
    AB XOR A'B XOR A'B' XOR B'A
    B(A XOR A') XOR B'(A' XOR A)

    we know that A XOR A' =1

    B XOR B'

    and from one of the XOR property, X XOR X' = 1
    THEREFORE B EQUALY 1?
    THE SOLUTION WOULD BE 1?
    let me know if that right?
     
  12. Oct 22, 2006 #11
    i think i did the 1st problem wrong...
    here is the simplied solution
    A'B xor BC xor AB xor B'C'
    becomes
    A'B xor AB xor BC xor B'C'

    A'B xor AB = B (we know that A A' =1)

    BC xor B'C'
    = (B xor C')(C xor B')

    B xor (B xor C')(C xor B')
     
  13. Oct 22, 2006 #12
    A'B xor BC xor AB xor B'C'

    this is just one possibility:

    step 1. - rearrange (correct)

    A'B xor AB xor BC xor B'C'

    step 2 - A'B xor AB is equivalent to just using B (correct), we have now

    B xor BC xor B'C'

    step 3 - BC xor B'C' is equivalent to B xor C' we are allowed to do this, since substituiting this will not alter the value of the overall truth table

    B xor B xor C'

    step 4 - B xor B will always be 0 we have now

    0 xor C'

    step 5 - 0 xor C' depends only on the value of C'

    result: C'

    this is ofcorse just one possibility.

    you got the B example right.

    A'B xor AB = B (we know that A A' =1)
    what has A A' got to do with it?
     
  14. Oct 22, 2006 #13
    Thank You So Much. That Really Helped.
    Thanks Everyone
     
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