Windows 7 serials

I just built a computer only to find out that windows 7 home premium only supports 16GB of RAM (I guess I'm stupid, honestly didn't know.) I activated windows on the computer, but am no longer using the [strike]serial number[/strike] Product Code in favor of another Ultimate code so i can use all my RAM (used it literally for 5 minutes). Can I still activate this serial on another computer given that I'm not using it on the one I just built? It's an SP1 system builder pack of W7 home premium.