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Truth table of NAND gate

  1. Nov 1, 2016 #1
    1. The problem statement, all variables and given/known data
    (a)

    bba80517b798.jpg

    e0bf5a3cb5c2.jpg

    The diagram represents a NAND gate with two inputs, T1 and T2, and an output X. Copy the truth table above and complete it.

    Show how a NAND gate can become a NOT gate.

    (b)

    681e31fb40ef.jpg

    Draw up a truth table for the combination of NAND gates shown above.

    2. The attempt at a solution
    (a) The truth table:

    4e5af0c98874.jpg

    A NAND gate is an AND and a NOT gate:

    combined_and_not.jpg

    (b) First of all, I shall add letters to the graph:

    9bc19d6a1af0.jpg

    I got two truth tables and not sure which one is correct.

    559af6128d28.jpg

    Are they both correct in this situation (so the problem has two solutions)? Looks like the answer depends on what combination does one put in the first two columns: 00 10 01 11 or 00 01 10 11 (specifically 10 01 or 01 10).
     
  2. jcsd
  3. Nov 1, 2016 #2

    NascentOxygen

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    Staff: Mentor

    Your truth tables are identical.

    I don't see any reason for duplicating column T2. One entry for T2 should suffice.
     
  4. Nov 1, 2016 #3
    Are you sure? In the left one the output is 0011 and in the second 0101. Maybe I miss something? This doesn't look identical...

    (I assume the (a) part is correct, right? Since you didn't mention it.)
     
  5. Nov 1, 2016 #4

    NascentOxygen

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    Staff: Mentor

    You have swapped 2 rows, that's all.
     
  6. Nov 1, 2016 #5
    But the output X is different, or it is acceptable?

    In other words both solutions are correct?
     
  7. Nov 1, 2016 #6

    NascentOxygen

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    Staff: Mentor

    There is only one solution; you have written it out twice.

    For each input combination there can be only one output. There are 4 possible input combinations, the order in which you document them in a table does not matter.
     
  8. Nov 1, 2016 #7
    withdrawn
     
    Last edited: Nov 1, 2016
  9. Nov 1, 2016 #8
    Well, the output in X is different in the tables, so I thought I got it wrong somewhere.
     
  10. Nov 1, 2016 #9
    withdrawn
     
    Last edited: Nov 1, 2016
  11. Nov 1, 2016 #10
    One input and one output? It's an inverter.
     
  12. Nov 1, 2016 #11

    NascentOxygen

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    Staff: Mentor

    Your outputs are listed in a different order only because the inputs have been listed in a different order.
     
  13. Nov 1, 2016 #12
    So in sum: both tables are correct and both solutions are acceptable?
     
  14. Nov 1, 2016 #13

    NascentOxygen

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    Staff: Mentor

    There is only one solution: the set of 4 outputs for 4 unique input combinations. Whatever way you tabulate these 4 lines is correct.
     
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