Last time I upgraded my computer (groan, I think I will be doing this again soon), I downloaded PS, "deactivated" the software on the old box, and activated the software on the new one. I think I also call tech support to make sure all was OK. Whether you change OS for Win to Mac or just get a new whatever you have now, the software will all need to be moved and re-registered. And, it is best to have it running on both the old and new machines so you can go through all the settings and preferences one by one to insure the new box does just what the old did.
Which raises a totally non-camera / non-canon rhetorical question: Why is this always such a pain in the you-know? If I sell you my car and get another, the registration changes are easy (usually just a couple of signatures) but with PS or any software of significance, it is very time-consuming at best.