Video Transcript
The diagram shows a logic circuit
consisting of three OR gates. A row of the truth table for this
circuit is shown below, indicating the output value for one of the possible
combinations of input values. What is the value of 𝑠 in the
table?
This question is asking us to work
out the value of the output in this combination of three OR gates. Before we start to tackle this
question, let’s remind ourselves how a single OR gate works.
Recall that an OR gate is a kind of
binary logic gate. It’s called a binary gate because
the inputs and output can take one of just two values, zero or one. An OR gate has two inputs and one
output. It’s called an OR gate because it
outputs a value of one if either this input or this input has a value of one. The gate also outputs a value of
one if both inputs are one. So in all these three cases, the
output will be one. An OR gate will only output a value
of zero if both inputs are zero.
In this question, we’ve been given
a combination of three OR gates. The OR gates are connected so that
the inputs to the third gate are the outputs of the first two gates. Let’s start by labeling the diagram
with the information given to us in the table. We know that input 𝐴 is zero,
input 𝐵 is one, input 𝐶 is zero, and input 𝐷 is one. We are told that the output of the
final gate is an unknown value 𝑠. To answer this question, we need to
work out whether 𝑠 is equal to zero or one. To do this, we can look at each OR
gate in turn.
To begin with, let’s look at this
OR gate here. We have one input with a value of
one and one input with a value of zero. So, what does this tell us about
the output of this gate? Well, recall that an OR gate will
output a value of one if any of its inputs have a value of one. Since this input here — that is,
input 𝐵 — has a value of one, we know that the output of this gate must be equal to
one. Now, let’s look at this gate
here. Again, we have one input with a
value of one and one input with a value of zero. So, just like before, we know that
this gate will also have an output value of one. Finally, let’s look at this third
gate here. The inputs to this gate are equal
to the outputs of the two gates we have already considered. That means that both of these
inputs to the third OR gate are equal to one.
Now, what does this tell us about
the value of this output 𝑠? We know that an OR gate outputs a
one if either or both of the inputs are equal to one. Since both of these inputs are
equal to one, the gate will output a value of one. This final output is the value of
𝑠, which is what we were asked to find. So, our final answer to the
question is that the value of 𝑠 is equal to one.
