The diagram shows three NOR gates, where the outputs of the first two NOR gates are
the inputs to the third. If input 𝐴 is one, input 𝐵 is zero, input 𝐶 is one, and input 𝐷 is one, what is
Okay, so here, we can see we’ve got two different NOR gates. And the outputs to these two NOR gates become the input to the third NOR gate. Having been given specific values for input 𝐴, input 𝐵, input 𝐶, and input 𝐷, we
need to work out what the output ends up being. Now to do this, we first need to be able to recall the behaviour of one single NOR
gate. So a NOR gate behaves according to this truth table. Let’s say that it has two inputs, input 𝛼 and input 𝛽. Then this table shows what the output will be of the NOR gate for each possible value
of 𝛼 and 𝛽.
Now, the way that a NOR gate works is that it’ll only produce an output of one if
neither input 𝛼 nor input 𝛽 are one. That’s why it’s called a NOR gate because only when both inputs are zero, the output
is one. Or in other words, neither input 𝛼 nor input 𝛽 can be one in order for the output
to be one.
Now onto that information, we can go on to looking at the question. So in the question, we’ve been told that input 𝐴 is one. So let’s write a one next to input 𝐴. We’ve also been told input 𝐵 is zero, so here’s a zero. Input 𝐶 is one. So we write that down as well. And input 𝐷 is one as well. So we write that here. We’ve been asked to calculate the value of the output. But we need to do this in stages.
First, let’s see what happens with this NOR gate and more specifically what the
output of that NOR gate ends up being based on this truth table. Now in this situation, input 𝐴 corresponds to input 𝛼. And input 𝐵 corresponds to input 𝛽. So we know that the value of input 𝐴 or the first output is one. And the value of input 𝐵 or the second output is zero. So we’re looking at this row of the table. The value of the first input is one. Second output is zero. And so the output of that NOR gate must be zero. Hence, we can write a zero down over here.
Now this zero being the output of the first NOR gate is going to be one of the inputs
to the second NOR gate. And then at this point, we can look at this NOR gate. Now in this situation, input 𝐶 corresponds to input 𝛼. And input 𝐷 corresponds to input 𝛽. And we’ve been told that the first input is one. And the second input is one as well. So we’re looking at this row of the truth table. The first input is one. The second input is one. And so the output is going to be zero. And hence, we can write down a zero for the output of this NOR gate. And once again, this zero is going to become an input for the final NOR gate.
At this point then, we’ve got an input of zero and another input of zero going into
the final NOR gate. So we can work out the output of this NOR gate by looking at this row of the truth
table because this time, the first input of the final NOR gate is zero, the second
input of the final NOR gate is zero, and so the output must be one. Hence, we can write down a one next to the output. But then, this output is the final output of the series of NOR gates.
And so we figured out our final answer which is that the value of the output is