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Logic Gates/ Truth Tables Trouble

  1. Aug 13, 2012 #1
    Hey guys im having todo a resit paper for a maths module i failed and ive come up against a question on my paper where im stomped and dont know if im down the right road or not. Its truth tables from Boolean equations.

    Question was:

    K = ( X + Y) . (X . Y)

    I Came up with:

    Code (Text):

    K [U][B]X[/B][/U] Y | X Y K | K
    1 0 0   1 1 1   1
    1 1 1   0 0 0   0
    1 0 1   1 0 0   0
    0 1 0   0 1 0   0
     
    Answer would be handy if i could get it and also where ive gone wrong and how todo it as theres a few more like this and worse. Ive bolded and underlined for Inverted attributes as the forum code doesnt let me space out to do the _ sign midline.
    Thanks
     
    Last edited by a moderator: Aug 13, 2012
  2. jcsd
  3. Aug 14, 2012 #2

    chiro

    User Avatar
    Science Advisor

    Hey Diearduk and welcome to the forums.

    Your table is wrong: you need to use the same x and y values for each operation. I will create a new table and create an extra variable corresponding to the inverted X.

    Code (Text):

    X Y Z = NOT X |  Z OR Y | X AND Y | (Z OR Y) AND (X AND Y)
    0 0  1           1            0                  0
    0 1  1           1            0                  0
    1 0  0           1            0                  0
    1 1  0           1            1                  1
     
    We can use distributive laws to show that:

    (NOT X + Y) . (X . Y) = (NOT X).X.Y + Y.X.Y = X.Y which is what we got above.

    You should use these kinds of simplifications to give another check of whether you get something symbolic that matches up with your truth table.
     
  4. Aug 14, 2012 #3
    Thanks Chiro, This forum and community looks great. Glad i could find it and thanks for your help :) Quick question tho was the Z meaning K? or was that the extra variable you made? i had a lecturer who really didnt educate anyone and just rambled on without explaining things :( meaning my whole class is pretty much as stomped as me.
     
  5. Aug 14, 2012 #4

    phinds

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    Gold Member
    2016 Award

    Look at his table. He specifically says Z=not X. It's just to make the simplification look less confusing.
     
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