So we're going to have to figure out what this nomenclature is. The first step is to determine which atom gets the one position. It turns out that the bridgehead atom must always be in the one position. Now, there are two different bridgehead atoms in all of these molecules, so the one you would pick would depend on maybe how close it is to a substituent. But regardless, you're always going to assign the one position to one of the bridgeheads.
Let's proceed and look at this compound. The bridgehead could be either this one or that one. In this case, there are no substituents, so it doesn't matter which one I pick, but one of those would have to get the one position. Let's just give the back one the one position. Then the next thing we do is look at the actual format of the name and you'll notice a few changes. Initially, the prefix used to be 'cyclo' if it was one ring, but now we exchange that for 'bicyclo'. Bicyclo simply indicates that it's a bicyclic compound. Anytime you have bridgehead atoms, anytime you have two rings or more conjoined together, it's considered bicyclic. Notice the carbon structure throughout; that's going to define the name of my alkane. If we wanted, we could just use these first few steps on this compound and say, well, this is a bicyclo compound because of the bridgehead atoms. It is also going to be an octane because it has eight carbons. Now that is not the correct numbering; I'm just counting to illustrate. So that means this would definitely be a bicyclooctane.
But now let's discuss these specific numbers in the middle, because I know you're wondering how to determine that. Essentially, we figure out how many carbons are inside these rings that are not bridgehead atoms. In this case, there are three rings. Remember, in a bridge compound there are three rings. So you would count the non-bridgehead atoms in ring number one, ring number two, and ring number three. Then we catalog them using periods and list them from largest to smallest. My largest ring here ends off with my smallest ring size there, and the middle one would be ring two.
Looking at this structure now, I have my bridgeheads labeled here. And then I see a few different rings. I'll call the bigger ring here number 1. Notice that I have three carbons that are not bridgehead atoms on that ring. This implies the ring size is three. Then the next ring over on this side would include two atoms that are not bridgehead atoms. Thus, the size of this ring is two. Finally, at the top, notice I only have one carbon between my bridgehead atoms. So, the ring size here is one. Now, I put them together in order of largest to smallest, showing that we've got an eight-membered structure with three carbons in one ring, two carbons in another ring, and one carbon in the last ring. That's what this color coding indicates.
Now about naming an unsubstituted, bicyclic structure. But what if we need to number it in terms of substituents? Suppose I have a methyl group coming off this location right here. What position does that methyl group occupy? Is it at 1, 2, or 8?