Solving truth tables with more than one output??

Discussion in 'Homework Help' started by RChang1202, Oct 11, 2014.

  1. RChang1202

    Thread Starter New Member

    Oct 11, 2014
    4
    0
    Hi Guys!

    I had to do a logic circuit to solve Y=3X. Below is the truth table.
    upload_2014-10-11_22-57-4.png
    To simplify the truth table a little bit I created the one below.... Lets focus on this one!
    upload_2014-10-11_22-57-25.png

    I couldn't find any info on how to solve this truth table. I know how to use minterms and maxterms for truth tables with single output, but I had no idea on how to use them for multiple outputs, so used Logic Friday to solve the truth table for me.

    These were the formula I got from Logic Friday for each of the four outputs :
    Z1 = A B;
    Z2= A B';
    Z3 = A' B + A B';
    Z4 = A' B + A B;

    By minimizing them I got:
    Z1 = A B;
    Z2= A B';
    Z3 = A B' + A' B;
    Z4 = B;

    I assembled the circuit using these four formula output and it worked perfectly.
    I though I could not find any info on how to solve these because they were going to be taught on the next chapter, maybe using K mapping, but now I still don't have any idea on how we got from this:
    upload_2014-10-11_22-57-25.png
    To this:
    Z1 = A B;
    Z2= A B';
    Z3 = A' B + A B';
    Z4 = A' B + A B;

    Can someone please tell me how are those formula obtained from and the procedure involved?

    Thanks!
     
  2. ScottWang

    Moderator

    Aug 23, 2012
    4,853
    767
    You should separate them to two parts, the first part are X,Y and second part are Z1,Z2,Z3,Z4.

    1. To connecting X,Y to logic gates and to Z1.
    2. To connecting X,Y to logic gates and to Z2.
    3. To connecting X,Y to logic gates and to Z3.
    4. To connecting X,Y to logic gates and to Z4.

    Drawing the block diagram first and using the logic gatess to replace them.
     
    Last edited: Oct 11, 2014
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  3. RChang1202

    Thread Starter New Member

    Oct 11, 2014
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  4. tshuck

    Well-Known Member

    Oct 18, 2012
    3,531
    675
    Where does A and B come in!? I didn't see those in the truth tables...

    You have X and Y as your input variables in one truth table and Y as the output of another one - always be aware of your variable names.

    If a variable has been used, use another one so that you (and the person grading you) don't get confused.

    Anyway, I will answer looking at this truth table:
    [​IMG]

    An easy way to look at it is to break it up into individual outputs (e.g.):
    truth_tables.png
    Which is roughly what you've gotten - no K-maps needed.
     
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  5. RChang1202

    Thread Starter New Member

    Oct 11, 2014
    4
    0

    Thaks!
    This is a more detailed explanation for someone having the same problem as me. Hope this can be useful for others.

    About the A and B... I copied the equations directly from Logic Friday and forgot to change the variable names, sorry about that!
     
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