Two Level OR-AND network

Discussion in 'Homework Help' started by tkecanuck341, Feb 16, 2008.

  1. tkecanuck341

    Thread Starter New Member

    Feb 16, 2008
    2
    0
    I am having some trouble creating a circuit to satisfy this truth table. The assignment is to create a two-level OR-AND and a two-level AND-OR circuit to satisfy the following truth table.

    x=x(a,b,c)
    a b c x
    0 0 0 1
    0 0 1 0
    0 1 0 0
    0 1 1 0
    1 0 0 0
    1 0 1 1
    1 1 0 0
    1 1 1 1

    The AND-OR circut was easy, and I got the following.

    (ac) OR (a'b'c')

    The OR-AND circuit is a bit harder, as I can't determine which OR circuits I can make that i can combine with an AND gate to produce the table. I've tried the gates (a+c)... (b XOR c')... and (a+b+c)', to give me:

    a+c = X
    b XOR c' = Y
    (a+b+c)' = Z

    a b c X Y Z
    0 0 0 0 1 1
    0 0 1 1 0 0
    0 1 0 0 0 0
    0 1 1 1 1 0
    1 0 0 1 1 0
    1 0 1 1 0 0
    1 1 0 1 0 0
    1 1 1 1 1 0

    As you can see, I can't figure out a way to combine any of these with an AND gate to make the above truth table.

    Can someone please let me know if there is a better way to approach this? Any help you can give would be greatly appreciated.

    Thanks
     
  2. tkecanuck341

    Thread Starter New Member

    Feb 16, 2008
    2
    0
    I think I figured it out.

    I get (b'+c)(a XOR c').
     
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