Video Transcript
The diagram shows a logic circuit consisting of three AND gates. How many of the inputs must have a value of one in order for the output to have a value of one?
The question gives us a diagram of a logic circuit containing three AND gates. The circuit has four inputs, which are labeled as A, B, C, and D. We can see that input A and input B go into this top AND gate, while C and D are the inputs to this bottom AND gate here. The output of each of these first two AND gates then becomes one of the inputs for this third AND gate over here. And then the output from this third AND gate is the overall output from this logic circuit. We’re told that we want this output to have a value of one. So let’s add this output value of one to our diagram.
We’re being asked to work out how many of the inputs, so that’s our A, B, C, and D, must have a value of one in order to get this output value of one. In order to work this out, we need to recall how an AND gate works. The output of an AND gate is one only if both of the two inputs to it have a value of one. Otherwise, so if either or both of the inputs is zero, then the output of the AND gate is zero. In fact, it’s called an AND gate because in order for the output to have a value of one, then the first input to the gate must have a value of one and the second input must also have a value of one. So let’s think about what this means for the circuit in this diagram.
In order for the output of this third AND gate, and therefore the output of the circuit, to have a value of one, then both of these two inputs to the AND gate must have a value of one. Now we’ve already seen that this top input comes from the output of this first AND gate here and that this lower input comes from the output of this AND gate. So then both of these two AND gates must have an output value of one. Since we know that the output of an AND gate will only be one if both inputs are one, then the only way that this output can be one is if both input A is one and input B is one. In the same way, the only way that this output can be one is if input C is one and input D is one as well.
If either of input A or input B had a value of zero, then the output of this first AND gate would be zero. This would mean that the upper input to this third AND gate would have a value of zero, and so its output would be zero. Likewise, if either of input C or input D had a value of zero, then this AND gate would have an output of zero. And so this third AND gate would have a lower input of zero, which would make its output zero.
So we can see that if any one of the inputs A, B, C, or D does not have a value of one, then the output of the circuit will not have a value of one. In other words, in order for this output to have a value of one, we require all four of these inputs to have a value of one. So our answer to the question is that the number of inputs that must have a value of one is four.
