The "hard problem" is talking about the thing that it's like to be you, to experience what is happening. I don't know about you, but I only experience one set of things happening at once, i.e. it doesn't feel like I am in two places at once or that there are two completely different versions of my life happening simultaneously.

If the physical thing that is conscious is the CPU, what are the contents of its consciousness if there are multiple interpretations of what it is computing?

Now maybe somehow there are in fact multiple consciousnesses inhabiting the CPU. I don't experience that though, so I don't have a positive reason to believe that that's true.