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Boolean's Algebra - SOP

  1. Dec 15, 2014 #1
    Can someone please explain why the F( X, Y ) is XY' + XY ? IMO , it is X'Y' + X'Y +XY' +XY .... or the author simplified it to become XY' + XY ? how to simplify it?
     

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  3. Dec 15, 2014 #2

    jedishrfu

    Staff: Mentor

    Use boolean algebra to reduce it. In boolean algebra X+X' = 1 and use algebra to extract common factors.

    Is this a homework assignment?
     
  4. Dec 15, 2014 #3
    no, i am studying myself during the holiday.
     
  5. Dec 15, 2014 #4

    jedishrfu

    Staff: Mentor

    Did my advice make sense?

    Boolean algebra rules are the same as ordinary algebra with the added concepts X=X'=1 and X.X'=0 and X=0 means X=false and X=1 means X=true. Engineers start with a truth table for a circuit, construct boolean expressions, reduce them down using boolean algebra ruls and then construct a circuit from the reduced expressions.
     
  6. Dec 15, 2014 #5
    i only managed to reduce it to XY +Y' +X'Y
    here's my working:
    (X'Y') + (X'Y) + (XY') + (XY)
    =XY +Y'(X' +X ) +X'Y
    = XY +Y' +X'Y
     
  7. Dec 15, 2014 #6

    jedishrfu

    Staff: Mentor

    what about the 1st and 3rd term? they have a common Y.
     
  8. Dec 15, 2014 #7
    continue form the previous post , i still didnt get the ans
    XY +Y' +X'Y = Y(X +X') +Y' = Y+Y'
     
  9. Dec 17, 2014 #8

    NascentOxygen

    User Avatar

    Staff: Mentor

    Hi Desmond. No one can explain it. It's a misprint. :oops:

    It is just the exclusive OR function, X'Y + XY'. It doesn't simplify, except you can write it as X ⨁ Y.
    Good luck with your self-study. http://thumbnails112.imagebam.com/37333/0363e9373324851.jpg [Broken]
     
    Last edited by a moderator: May 7, 2017
  10. Dec 17, 2014 #9
    I noticed that theF(X , Y) is the outcome of the addition of the last two. *correct me if I m wrong* , why it only involve the addition of last two term? Why not also the first two terms??
     
  11. Dec 17, 2014 #10

    NascentOxygen

    User Avatar

    Staff: Mentor

    It's a misprint. F(X,Y) is true when either of these is true: X'Y or XY'
     
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