...that you could use the Product Key to install Windows 8 on a different PC using the clean install method.
See my article: The complete guide to a Windows 8 clean installation
As far as the 32-bit vs. 64-bit goes, I don't have a definitive answer. My first impression was that the bit version you ended up with would match the bit version of the system you used to run the Upgrade Assistant.
For example, if you ran the Upgrade Assistant on a 32-bit version of Windows 7, you'd get a 32-bit version of Windows 8 or if you ran the Upgrade Assistant on a 64-bit version, you'd get a 64-bit version.
Now, if that is indeed the case, you could run into a problem in the scenario you propose... i.e. you download a 64-bit version of Windows 8 and your old PC is a 32-bit system.
I'll look around and see if I can get anymore detailed information...
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