I can't speak to PI being 64 bit only, but as for the other factors you need the following:
1. 64 bit CPU, single/dual/quad cores doesn't matter as long as it understands 64 bit instruction sets.
2. OS must also be 64 bit supported, and typically can only be installed if the CPU is 64 bit comp.
If you have a 64 bit CPU and running an OS as 32 bit; then you are more than likely not going to be able to install a 64 bit piece of software successfully/easily.
I'm pretty sure 7.11 PI is 32 bit; not sure about 7.3/7.31/7.4 PO though.