Vista Home Premium x64 -> Ultimate x64 ??

I bought the Vista Ultimate package that contains both x64 & x32 bit DVDs.
I'm running Home Premium (Athlon 64 X2 Dual Core proc) and would like to
upgrade. When I open system properties, System type displays as: 32-bit
Operating System. Is it possible I'm running a 32-bit OS on a 64-bit machine?

Second question: when I try upgrading (inserting the 64-bit DVD) I get
message that I can't upgrade but must boot from DVD. I boot from DVD and the
upgrade option is disabled. Is it possible that I'm running the 32-bit
version of Vista Home Premium and must upgrade using the 32-bit DVD? Can I
than upgrade to the 64-bit version of Vista Ultimate? I hate to have to start
all over and rebuild by system.

Thanks for any help