Video Transcript
The diagram shows two AND gates, where the output of the first AND gate is one of the inputs to the second. If input A is one, input B is zero, and input C is one, what is the output?
Okay, so we’ve got a diagram showing a logic circuit containing two AND gates. The question tells us the values of the three inputs to the circuit. So let’s add those values to the diagram. We’re told that input A is one, input B is zero, and input C is one. We are being asked to work out the output of this logic circuit. Since the circuit is constructed out of AND gates, we’re going to need to recall how an AND gate works. We can recall that the output of an AND gate is one only if both of its inputs are one. Otherwise, for all other combinations of inputs, the output is zero. The reason that it’s called an AND gate is because in order for the output to be one, the first input must be one and the second input must also be one.
Since each of the two inputs for an AND gate can be either zero or one, then there are four possible pairs of values for the inputs. We can have both inputs as zero or the first input as zero and the second as one, or we can have the first input as one and the second as zero, or finally both inputs could be one. Since an AND gate only has an output of one if the values of both of the inputs are one, then in this output column for an AND gate, the only row that will have a value of one is this bottom row where both of the two inputs are one. In all of the other three rows, the output will be zero, since in each case, at least one of the two inputs has a value of zero.
In the diagram we’re given in this question, the first AND gate has a first input, input A, with a value of one and a second input, input B, with a value of zero. This situation corresponds to the third row in our logic table, first input one, second input zero, and so the output is zero. This output from the first AND gate then becomes one of the inputs to the second AND gate. So if we now look at the second AND gate, we see that its first input is zero. That’s the value that was output from the first AND gate, and its second input is input C, which we’re told has a value of one.
The second row in our logic table says that when the first input is zero and the second input is one, the output will be zero. This output from the second AND gate is then the overall output from the logic circuit shown in the diagram. And so our answer to the question is that the output of the circuit is zero.
