There is no upgrade from 32-bit to 64-bit. 64-bit requires a clean install of the Windows 7 system.
The real question is whether your system was designed to support 64-bit. Does the system manufacturer have 64-bit drivers for all the hardware and functions of your system? You need to check the manufacturer's website and check if they are providing
all the drivers necessary for your system to be fully functional. Windows 7 will not have all your system drivers.
The main item to consider is whether you can increase the system memory. 3GB is enough to run 64-bit, but more RAM would enhance the performance of the system.
You should also run the Windows 7 Upgrade Advisor:
http://windows.microsoft.com/en-us/windows/downloads/upgrade-advisor
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