Question Video: Evaluating the Output of Four NOT Gates in Series Physics

Four NOT gates are connected together in series. If the input of the first NOT gate is 0, what will the output of the final NOT gate be?

03:23

Video Transcript

Four NOT gates are connected together in series. If the input of the first NOT gate is zero, what will the output of the final NOT gate be?

Alright, so we’re told that we’ve got four NOT gates connected in series. So let’s draw a diagram to show these gates. The symbol for a NOT gate is a triangle oriented so that one of its corners is pointing to the right with a small circle on the end of this point. We were told that we’ve got four such NOT gates connected together in series. Connected in series means that the gates are placed one after another in a line like this. It means that the output from the first NOT gate becomes the input for the second NOT gate. Similarly, the second NOT gate’s output becomes the third NOT gate’s input, and the third NOT gate’s output becomes the fourth NOT gate’s input. In other words, starting from the left, the output from each NOT gate becomes the input for the next one in the line.

We are told that the input for the first NOT gate is zero. So let’s add this input value to our diagram. To work out what this final output value will be, we need to follow this initial input of zero and see what happens to it as it goes through each NOT gate in the line. In order to do this, we need to recall how a NOT gate works. We can recall that a NOT gate acts to negate its input value. This means that for a NOT gate, an input value of zero becomes an output value of one, while an input value of one becomes an output value of zero. What we’ve drawn out here is known as the truth table for a NOT gate, and we can use this to see what happens to our input value.

We begin with an initial input of zero, and this is the input for the first NOT gate in the series. We can see from our table that an input value of zero gives us an output value of one. So let’s add this to our diagram. We can see that this output of one then becomes the input for the second NOT gate. Again, looking at our logic table, we can see that an input of one gives an output of zero. So let’s put this on our diagram. This output then becomes the input for the third NOT gate. And we know that an input of zero means an output of one. Adding this to our diagram, we can then see that the fourth and final NOT gate has an input value of one. And we know that an input of one means an output of zero. So we know that the output after the final NOT gate is zero. And this value of zero is then our answer to the question.

As an aside, it’s worth noticing that we would get the same result for any even number of NOT gates connected in series. Since a NOT gate works by negating the input value to give the output, then two NOT gates in series means that the initial input gets negated twice, once by each NOT gate. And as we can see from the first half of this diagram, the output value after two NOT gates is the same as the input value. Then for any even number of NOT gates connected in series like this, we could imagine pairing the NOT gates off, and then effectively within each pair, the second NOT gate acts to undo the effects of the first one. Then the output after each pair of NOT gates must be the same as the input value to that pair.

This means that no matter how many pairs of NOT gates there are, as long as there’s an even number of NOT gates in total, we can pair them all off so that at the end of all of the pairs, the output must be the same as the initial input.

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