I have two student/faculty upgrade discs of Windows 7 Pro that I got from a university bookstore: one is clearly labeled 32-bit, and the other is labeled 64-bit. My desktop is running Windows 7, installed from the 32-bit disc and using that product key. I'm going to upgrade from 2GB RAM to 8GB soon, so I'll need 64-bit Windows 7. The product key for the 64-bit disc is already used on another computer, so it is possible to use the 32-bit product key to install the 64-bit disc?
tl;dr version: Are Windows 7 product keys architecture-independent?
tl;dr version: Are Windows 7 product keys architecture-independent?