Holding Windows-key and press the "Pause/Break" key will bring up the info about the type of processor and OS you're running, apart from others.
Here're are two articles which might be helpful about the 32/64-bit OS and apps. etc.
32 bit and 64 bit explained
How Windows 7 / Vista 64 Support 32 bit Applications
My understanding is that: to run 64-bit OS, the processor must be 64-bit, but the 64-bit processor can accept either 32 or 64bit OS.