using xor gate as an or gate?

Discussion in 'Homework Help' started by coolguylol, Dec 14, 2012.

  1. coolguylol

    Thread Starter New Member

    Dec 14, 2012
    1
    0
    I was wondering how one would rewrite f= x(y+z),using only AND and XOR gates, into
    f=x(yz XOR y XOR z)?

    xy+xz
    xy(z+NOTz)+x(y+NOTy)z
    x(yz+(y XOR z))

    Thank you.
     
  2. WBahn

    Moderator

    Mar 31, 2012
    17,788
    4,808
    When you have:


    f = A*g

    and you want to show that

    f = A*h

    you only need to show that g = h. So you only need to show that

    (y+z)=(yz XOR y XOR z)

    The approach you are taking is fine.

    (y+z) = (y(z+z') + (y+y')z)
    (y+z) = (yz+yz' + yz+y'z)

    (y+z) = (yz + (yz'+y'z))

    At this point, you might make the truth table for the right hand side and that might give you a clue as to how to proceed. You might also start with the goal and see if you can work it back to the above.

    (yz XOR y XOR z)

    You can group this three ways:

    (yz XOR (y XOR z))
    ((yz XOR y) XOR z)
    ((yz XOR z) XOR y))

    So exapnd these and play with them a bit. Show what you get, even if t isn't all the way, and we'll go from there.
     
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