WEBVTT
00:00:00.810 --> 00:00:04.360
The diagram shows a logic circuit consisting of three OR gates.
00:00:04.800 --> 00:00:11.870
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.
00:00:12.480 --> 00:00:14.600
What is the value of 𝑠 in the table?
00:00:16.000 --> 00:00:21.670
This question is asking us to work out the value of the output in this combination of three OR gates.
00:00:22.430 --> 00:00:27.150
Before we start to tackle this question, let’s remind ourselves how a single OR gate works.
00:00:27.940 --> 00:00:30.820
Recall that an OR gate is a kind of binary logic gate.
00:00:31.380 --> 00:00:37.190
It’s called a binary gate because the inputs and output can take one of just two values, zero or one.
00:00:38.060 --> 00:00:40.850
An OR gate has two inputs and one output.
00:00:41.440 --> 00:00:48.670
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.
00:00:49.430 --> 00:00:52.910
The gate also outputs a value of one if both inputs are one.
00:00:53.470 --> 00:00:56.500
So in all these three cases, the output will be one.
00:00:57.110 --> 00:01:01.750
An OR gate will only output a value of zero if both inputs are zero.
00:01:02.470 --> 00:01:05.960
In this question, we’ve been given a combination of three OR gates.
00:01:06.460 --> 00:01:12.190
The OR gates are connected so that the inputs to the third gate are the outputs of the first two gates.
00:01:13.170 --> 00:01:17.210
Let’s start by labeling the diagram with the information given to us in the table.
00:01:18.410 --> 00:01:24.990
We know that input 𝐴 is zero, input 𝐵 is one, input 𝐶 is zero, and input 𝐷 is one.
00:01:25.730 --> 00:01:29.670
We are told that the output of the final gate is an unknown value 𝑠.
00:01:30.070 --> 00:01:34.580
To answer this question, we need to work out whether 𝑠 is equal to zero or one.
00:01:35.600 --> 00:01:38.270
To do this, we can look at each OR gate in turn.
00:01:38.960 --> 00:01:41.540
To begin with, let’s look at this OR gate here.
00:01:42.170 --> 00:01:46.070
We have one input with a value of one and one input with a value of zero.
00:01:46.780 --> 00:01:49.610
So, what does this tell us about the output of this gate?
00:01:50.700 --> 00:01:56.110
Well, recall that an OR gate will output a value of one if any of its inputs have a value of one.
00:01:56.590 --> 00:02:03.780
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.
00:02:04.430 --> 00:02:06.150
Now, let’s look at this gate here.
00:02:06.620 --> 00:02:11.010
Again, we have one input with a value of one and one input with a value of zero.
00:02:11.530 --> 00:02:16.380
So, just like before, we know that this gate will also have an output value of one.
00:02:17.550 --> 00:02:19.740
Finally, let’s look at this third gate here.
00:02:20.220 --> 00:02:25.070
The inputs to this gate are equal to the outputs of the two gates we have already considered.
00:02:25.970 --> 00:02:29.690
That means that both of these inputs to the third OR gate are equal to one.
00:02:30.260 --> 00:02:33.960
Now, what does this tell us about the value of this output 𝑠?
00:02:34.570 --> 00:02:39.860
We know that an OR gate outputs a one if either or both of the inputs are equal to one.
00:02:40.450 --> 00:02:45.200
Since both of these inputs are equal to one, the gate will output a value of one.
00:02:45.740 --> 00:02:49.830
This final output is the value of 𝑠, which is what we were asked to find.
00:02:51.030 --> 00:02:55.920
So, our final answer to the question is that the value of 𝑠 is equal to one.