My PC is now running 32-bit Windows 7, and I want to upgrade it to 64-bit, but I don't have disc. Can I upgrade to Windows 7 64 bit without any CD? If yes, what would I need to do?
Unfortunately, this is not possible. To convert from 32-bit to 64-bit requires a full reinstall of the operating system.
Thankfully, 32-bit keys are also valid for 64-bit installations (source) so you would be allowed to do this.
If you have a legitimate key, you can get your hands on an ISO for installation here: http://www.mytechguide.org/766/download-windows-7-iso-official-links/
This site links to the Digital River download site, which is the official retail partner for Microsoft content provisioning and the ISOs contained within it are the same ones you would be directed to if you bought the software online from Microsoft.
Please be advised though, that installing this software without a valid license is illegal!