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.
