Video Transcript
Each of the diagrams shows a logic circuit consisting only of AND gates. Which of the diagrams shows a circuit where the output has a value of one?
Okay, so this question has given us four logic circuits to consider. In each case, there’s a bunch of inputs to the circuit on the left-hand side and an output on the right. Our task here is to work out in which of these four circuits the output has a value of one. Since each of these circuits consists only of AND gates, then to answer this question, we should begin by recalling how an AND gate works.
An AND gate is a kind of binary logic gate. Binary means that each input and output to the gate can take just one of two values. Those values are zero and one. An AND gate takes two input values and returns a single output. This output has a value of one only if both of the inputs are one. In all other cases — that is, if either or both of the inputs have a value of zero — the output of the AND gate is zero. It’s called an AND gate because, in order to get an output of one, this input must be equal to one and this input must also be equal to one.
With this information, we can write out the logic table for an AND gate. This shows the output of the gate for each possible combination of inputs. The four possible input combinations are zero and zero, zero and one, one and zero, and one and one. Since we know an AND gate only gives an output of one when both inputs are one, then the output in these first three cases must be zero, and only this fourth row in the table has an output of one.
We can now use the information in this table to work out the value of the output for each of the logic circuits given to us in the question. Let’s begin with the circuit in option (A). We can see that this logic circuit consists of three AND gates. There’s these two over here on the left. Then, the outputs from each of these two gates become the inputs for this third AND gate here on the right.
Let’s start by looking at this top left-hand AND gate. We see that the first input is zero and the second input is one. This corresponds to the second row in our logic table. We see that the output of the AND gate in this case has a value of zero. We know that this output is then the first input to the right-hand AND gate.
Now let’s look at the lower left-hand gate. The first input is one, and the second input is zero. This corresponds to the third row of the logic table, which tells us that this AND gate produces an output value of zero. This output then becomes the second input to the right-hand AND gate. We see then that this right-hand gate has both input values equal to zero. This matches the first row of the logic table, and so we know that the output value is zero. This is the overall output of this logic circuit. We know then that logic circuit (A) produces an output value of zero. Since we’re looking for a circuit that has an output value of one, this is not our answer. Let’s move on then to the logic circuit in option (B).
We’ve got three AND gates over on the left of this circuit. The outputs from the top two then become the inputs for this AND gate here. Then, the output from this gate, along with the output from the bottom left-hand AND gate, become the inputs for this right-hand AND gate.
Now, we’re going to work through this logic circuit a little quicker than we did for the last one. The key point to remember is that the output of an AND gate will only be equal to one if both inputs are one. If either input to an AND gate has a value of zero, the output of that gate will be zero. The top two AND gates on the left of the circuit in option (B) both have both of their inputs equal to one. The output from each of these AND gates will therefore be equal to one. These two outputs are the inputs for this AND gate here. Since both inputs have a value of one, the output here will also have a value of one. This gives us the first input for the right-hand AND gate.
To get the second input, we need to look at this bottom left-hand gate. It has one input of one and one input of zero. Since we don’t have both inputs equal to one, then the output of this AND gate will be equal to zero. This is the second input for the right-hand gate. This AND gate therefore has one input of one and one input of zero. The output of this gate will therefore be zero. This is the overall output from the circuit. So we know then that option (B) is not our answer. Let’s move on to option (C).
This left-hand AND gate has both inputs equal to one. It therefore has an output value of one. This output then becomes the first input for the right-hand AND gate. The second input to this right-hand gate is this value of one. Both inputs to this right-hand AND gate then are equal to one, and so its output value is one. This value is the output from the logic circuit. This circuit therefore does produce an output value of one. It’s looking then like option (C) is our answer. Let’s have a quick look at option (D), though, just to make sure.
The top left-hand AND gate in this circuit has two inputs with a value of one. The output of this gate is therefore one. The bottom left-hand AND gate has one input of zero and one input of one. So the output of this gate is zero. These two outputs become the inputs for this right-hand AND gate. This gate then has one input of one and one input of zero. The output, which is the overall output of the circuit, therefore has a value of zero. This means that option (D) is not our answer.
We have found then that the logic circuits shown in options (A), (B), and (D) all produce an output with a value of zero. The only logic circuit where the output has a value of one is the circuit shown in option (C). And so, we choose option (C) as our answer.
