Video Transcript
The diagram shows a logic circuit
consisting of three OR gates. How many of the inputs must have a
value of zero in order for the output to have a value of zero?
We’ve got a diagram here that shows
a logic circuit with three OR gates in it. The circuit has four inputs, which
are labeled as 𝐴, 𝐵, 𝐶, and 𝐷. Inputs 𝐴 and 𝐵 are the two inputs
to this upper OR gate on the left, while inputs 𝐶 and 𝐷 go into this lower OR
gate. The output from each of these
left-hand OR gates then becomes one of the two inputs for this OR gate over here on
the right. Then, the output from this
right-hand OR gate is the overall output of this logic circuit as a whole.
We’re being asked to consider the
case where this output has a value of zero. Our job is to work out how many of
these four inputs need to have a value of zero in order to get this output value of
zero. In order to do this, since these
inputs and this output are connected by this circuit consisting of OR gates, then
we’re going to need to recall how an OR gate works.
An OR gate is a type of logic gate
that gives an output of one if either of the two input values or both of them have a
value of one. Otherwise, so if both of the inputs
are equal to zero, then the output of an OR gate is zero. We can use this information in
order to draw a truth table for an OR gate. This truth table is a table which
lists all of the different possible combinations of the two inputs to the OR gate,
along with the output value that will be produced by each such pair of inputs.
If both of the two inputs to an OR
gate are equal to zero, then it’s not true that either or both inputs are one. And so, we’re looking at the second
bullet point here, which tells us that the output will be zero. If the first input is zero, but the
second input is one, then now this first bullet point is true because we do have one
of the inputs equal to one. And so, the output from the OR gate
will be one. Likewise, if the first input is one
and the second input is zero, then again we’ll have an output of one because this
first bullet point doesn’t distinguish between the two inputs. It’s just that to get an output of
one, at least either one of the two inputs has to be equal to one.
The final case to consider is when
both of the two inputs have a value of one. Again, this first condition is met
because it says that either or both of the inputs must be equal to one in order to
get an output of one. And so when both inputs are equal
to one, we know that the OR gate will give an output of one. Now that we’ve written out this
truth table, we can use it to help us work out what’s going on in this logic
circuit.
We’ll start by considering this OR
gate on the right-hand side of the circuit. We know that this gate has to have
an output with a value of zero. If we look at our truth table, we
can see that the only way to get an output of zero from an OR gate is if both of the
two inputs have a value of zero. So then both of the inputs to this
right-hand OR gate must be equal to zero. We know that the top input is the
output from the upper left-hand OR gate, while the bottom input is the output from
the lower left-hand OR gate. What this means is that both of
these left-hand OR gates must have an output value of zero.
Now, as we’ve already seen, we know
from our truth table that the only way to get an output of zero from an OR gate is
if both of the two inputs are equal to zero. So, for this upper left-hand OR
gate with an output value of zero, both of its inputs, so that’s input 𝐴 and input
𝐵, must be equal to zero. Similarly, since the lower
left-hand OR gate also has an output value of zero, then its inputs, input 𝐶 and
input 𝐷, must also be equal to zero.
What we found is that in order to
get this output value of zero, all four of these inputs must have a value of
zero. So, our answer is that in order for
the output to have a value of zero, the number of inputs which must have a value of
zero is equal to four.
