Truth table of NAND gate

  • #1
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Homework Statement


(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).
 

Answers and Replies

  • #2
NascentOxygen
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Your truth tables are identical.

I don't see any reason for duplicating column T2. One entry for T2 should suffice.
 
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  • #3
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Your truth tables are identical.

I don't see any reason for duplicating column T2. One entry for T2 should suffice.
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.)
 
  • #4
NascentOxygen
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You have swapped 2 rows, that's all.
 
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  • #5
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You have swapped 2 rows, that's all.
But the output X is different, or it is acceptable?

In other words both solutions are correct?
 
  • #6
NascentOxygen
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But the output X is different, or it is acceptable?

In other words both solutions are correct?
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.
 
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  • #8
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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.
I think you may be making this problem harder than it needs to be.
Well, the output in X is different in the tables, so I thought I got it wrong somewhere.
 
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  • #10
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How many inputs and outputs does a NOT have?
One input and one output? It's an inverter.
 
  • #11
NascentOxygen
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Well, the output in X is different in the tables, so I thought I got it wrong somewhere.
Your outputs are listed in a different order only because the inputs have been listed in a different order.
 
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  • #12
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Your outputs are listed in a different order only because the inputs have been listed in a different order.
So in sum: both tables are correct and both solutions are acceptable?
 
  • #13
NascentOxygen
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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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