You can't upgrade from a 32-bit system to a 64-bit system. You can, for example, upgrade from 32-bit Home Premium to 32-bit Professional, but not from a 32-bit to a 64-bit, regardless of edition.
So what you can do is replace your existing Windows installation. You have to back up your existing data, and then start your computer with the DVD and perform a "clean installation", which means erasing the existing data in the process. Then you have to return your data from backups, and re-install your applications.
You should be able to use your existing Windows 7 product key so long as the 64-bit edition you install is the same as your existing one (i.e., Home Premium to Home Premium).
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