Windows 7-32 upgrade to 64 bit.

What do you mean by BIOS upgrade to 64 bit? Your CPU (Processor) must be 64 bit capable before you can run 64 bit Windows.

You will have to do a clean installation, there is no in place upgrade path from Windows 7 32 Bit to 64 bit.

Using the Windows 7 64 bit disk, install the Windows 7 Windows Easy Transfer Utility from the DVD (To find it, just navigate to x:\support\migwiz, 'x:' represents the name of your disk drive. In this folder, you will see a collection of files, the important one you need to look for and double click is 'migsetup'.) , run it and create a WET file (Windows Easy Transfer file), if you have an external hard disk, you can have it stored there so you can access it later when you do a clean install of Windows 7 64 bit disk.

Once you have done that, simply do a clean install of Windows 7 64 bit disk. In Windows 7 64 bit disk, launch Windows Easy Transfer, follow the on screen wizard, point to where you stored the the WET file (external hard disk), and it will restore your personal files and settings. Reinstall any necessary applications.

http://www.notebooks.com/2009/10/07/using-windows-easy-transfer-in-windows-7/

32 vs 64 bit
http://windows.microsoft.com/en-US/windows7/32-bit-and-64-bit-Windows-frequently-asked-questions

Is my PC running the 32-bit or 64-bit version of Windows?
      http://windows.microsoft.com/en-us/windows7/find-out-32-or-64-bit

http://windows.microsoft.com/en-US/windows7/Installing-and-reinstalling-Windows-7

Windows 7 64 bit comes in handy when you need to address at least 4 GBs or more of RAM. Windows 7 32 bit can utilize up to 3.2 GBs of RAM. Because the memory address space is much larger for 64 bit Windows, that means, you need twice as much memory than 32 bit Windows to accomplish some of the same task, but you are able to do so much more, you can have more applications open, do things like run an Antivirus scan in the background without it affecting your system performance. Windows 7 64 bit is more secure too, malicious code cannot easily infiltrate it, drivers are more reliable since they must be signed before they can work with 64 bit Windows 7.

As for compatibility, you will need 64 bit device drivers for any hardware devices you might have. Also, there is no 16 bit subsystem in Windows 7 64 bit, which means, your applications must be 32 bit only, not 16 bit installer or uninstallers.