# Truth table of NAND gate

## Homework Statement

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

2. The attempt at a solution
(a) The truth table: A NAND gate is an AND and a NOT gate: (b) First of all, I shall add letters to the graph: I got two truth tables and not sure which one is correct. 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).

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NascentOxygen
Staff Emeritus

I don't see any reason for duplicating column T2. One entry for T2 should suffice.

• moenste

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.)

NascentOxygen
Staff Emeritus
You have swapped 2 rows, that's all.

• moenste
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?

NascentOxygen
Staff Emeritus
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.

• moenste
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• moenste
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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• moenste
How many inputs and outputs does a NOT have?
One input and one output? It's an inverter.

NascentOxygen
Staff Emeritus
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.

• moenste
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?

NascentOxygen
Staff Emeritus
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