Four NOT gates are connected in series. How many different combinations of input values are there for these gates?
So we’re told that we’ve got four NOT gates connected together in series. Let’s draw a diagram to show what this arrangement looks like. We can recall that the symbol for a NOT gate is a triangle oriented so that one of its corners is pointing to the right. And then, on this rightward-pointing corner there’s a small circle. We can also recall that a NOT gate works by taking a single input value and negating it. This means that each NOT gate has one input and one output. We are told that we’ve got four of these NOT gates connected in series, which means they’re joined one after the other in a line like this.
We can see that in this arrangement, the first NOT gate’s output then becomes the input for the second NOT gate. Similarly, the output from this second NOT gate then becomes the input for the third NOT gate, while the output from this third gate becomes the input for the fourth one. So, overall then for this arrangement of gates, there’s one input to the system over here on the left and one output over on the right. It’s this input to the system that we’re being asked about in this question. Specifically, we are asked for these four NOT gates. How many different combinations of input values there are?
We can recall that for any kind of logic circuit, each input can either have a value of zero or a value of one. So there’re two possible values for each input to a circuit. We know that this particular logic circuit or part of a circuit has just one input. So we’ve got one input which can take either of two possible values. This means that the number of input combinations to this circuit is two, where these two possibilities are that the single input has either a value of zero or a value of one.