Easy Bollean Algrebra

Discussion in 'Homework Help' started by smb3418, May 5, 2007.

  1. smb3418

    Thread Starter New Member

    May 5, 2007
    2
    0
    Ok al I want to know is how this boolean expression is simplified to the final answer, I can prove it to myself in a truth table, but that takes too much time.

    Here it is

    x*y+not(x)*z+y*z

    simplifies to
    x*y+not(x)*z

    Thanks

    Scott

    My first post
     
  2. thingmaker3

    Retired Moderator

    May 16, 2005
    5,072
    6
    I don't think that's right...
     
  3. Salgat

    Active Member

    Dec 23, 2006
    215
    1
    x*y+not(x)*z+y*z
    =
    x*y + z(not(x)+y)
    x*y + z(not(x)+xy) - since not(x) + y = not(x) + x*y
    x*y + z*not(x) + z*x*y
    x*y + z*not(x)


    I think thats right..?
     
  4. BrianH

    Active Member

    Mar 21, 2007
    43
    0
    Well, your answer is definitely good but I can't seem to follow your method. It's a pain that we can't write these things out more clearly I think. It'd be good if we could use a font where they had Not A's and NotB's etc in them.

    I think the way to proceed with that problem is to use the Race Hazard Theorem. I think I'll take a look at this later on in the afternoon and see what I can come up with.

    Brian
     
  5. Salgat

    Active Member

    Dec 23, 2006
    215
    1
    x*y+not(x)*z+y*z

    =

    x*y + z(not(x)+y)
    - z is ANDed to both y and not(x), so you can put the two in parenthesis as being ORed

    x*y + z(not(x)+x*y)
    - since not(x) + y = not(x) + x*y (its a theorem)

    x*y + z*not(x) + z*x*y
    - converting it all back out by ANDing z to not(x) and z to x*y

    x*y + z*not(x)
    - since x*y already exists, the z in z*x*y becomes optional and can be removed
     
  6. recca02

    Senior Member

    Apr 2, 2007
    1,211
    0
    and here is the proof for that (since i cudnt digest it so i tried,my knowledge is basic and i dont remember much of digital electronics i learned myself for a brief period)

    a' + ab = a'(1+b) +ab --------( 1+b)=1
    = a' + a'b +ab
    = a' + b(a' + a)
    = a' + b(1)
    = a' + b
     
  7. smb3418

    Thread Starter New Member

    May 5, 2007
    2
    0
    Sweet

    Thanks a lot guys
     
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