You could search google/newegg for your particular processor, if you know it by name, and read the specs. The specs on your processor says: 64-Bit Support: Yes.
http://www.newegg.com/Product/Product.aspx?Item=N82E16819103254
But i'd vote for someone else's answer if they could give a quick and easy way to check this without having to know your processor's model. Maybe it says in the bios on boot up?
As far as x86 processors are concerned, the simplest explanation is that a 32bit processor's general-purpose registers can hold integer values from 0 through (2^32)-1 (4,294,967,295), inclusive, or from -2,147,483,648 through 2,147,483,647, inclusive. This means it can address only that many bytes of virtual address space (4 GB).
An x86 64bit processor's registers can work with numbers from 0 through to (2^64)-1 (18,446,744,073,709,551,615), giving it, in theory, a much larger virtual address space.
To continue to your n-bit question: It will simply be able to work with numbers on 2^n.
Wikepedia has a good series of articles about bit width and the maths behind it all.
Best Answer
Your question is architecture specific. x64 is essentially an extension to x86 architecture. It supports a 64 bit address space. It provides some new instructions and new registers.
You can run 32-bit x86 Windows on an x64 machine. Note that you can't do this on Itanium 64-bit systems.