Does my processor dictate 32-bit vs 64-bit Windows operating system?

"Here's a spec chart for Intel Core2 Quad processors. According to the chart, your CPU does handle 64-bit OS's (Q9450, link to full specs), so you can install whichever you like.

As others have pointed out, once you're on a 64-bit OS, increasing RAM to 8GB will work if the motherboard supports it."

"Your processor is either 64 or 32 bit. I believe all the c2q range is 64bit, so you should be fine to upgrade.
Additionally, you can go from 4GB of RAM to almost any number you can think of :)"