Core 2 Duo T5870 and windows xp 32 bit??

[nmakes]

I have a compaq 510 notebook PC which has intel core 2 duo t5870 processor (@ 2Ghz, 2MB L2).
The vendor from whom we bought gave us windows xp 32 bit installed in it.
Lately I discovered that it is a 64 bit processor. So, I think I need a 64 bit OS to run it at its top speed. isnt it?
BTW, please tell me if I'm right. core 2 duo T5870 is a 64 bit processor, right?
AND, Is there any way by which I can speed up my notebook without any external config. Eg. overclock or share more video memory etc.?
ALSO, every processor manufacturer claims to have certain technologies. So, is there any such technology in my processor which I can exploit?

THANK YOU IN ADVANCE!!! :D

Specs:
Intel core 2 duo @ 2GHz, 2MB L2 cache
2 GB RAM
No graphics card. Integrated graphics @ 384 MB.

[caperjack]

if it were mine i would add more ram and put win7 64bit on it to speed it up

[JorgeM]

Windows XP support expires in less than 11 months and for that reason especially, you should consider caperjack's suggestion.

[nmakes]

Yeah... I mean, will the 64 bit thing work? cuz my vendor told me that it's a 32 bit processor...

[nmakes]

Actually, I was thinking of assembling a budget PC this June. So, I don't want to invest any more on this. This is the wishlist: http://www.flipkart.com/wishlist/navking.venkat7-7098

Processor: AMD FX 8350
Graphics: ATI Radeon HD 6670 2GB
Mobo: MSI 970A-G46
RAM: Corsair Vengeance 8GB
HDD: Seagate Barracuda 1TB

Can you please suggest a better config which would contain a case, monitor and still be less than 35,000 Rs (639$).
PS: I want the processor, ram and graphics card to be at least this equivalent or better.

[BigPaw]

The CPU is 64 bit.

If you would like to take advantage of your computer's 64 bit architecture then upgrade your RAM to at least 4GB (at least) dual channel. Install a 64 bit version of Windows 7 or 8 depending an your preference.

[nmakes]

Yeah. That's exactly what I meant. I wanted to take the advantage of the 64 bit architecture! Thanks for giving words to my emotions. ;)
So, I think I have no other solution. So I guess this question is solved. Thanks to everyone!

[nmakes]

I guess that was some advertisement.