upgrade/replace non genuine windows 7 ultimate with genuine home premium

Hi there, right now I have a non genuine version of Windows 7 Ultimate installed, I'm looking to replace it with a genuine copy of Windows 7 home premium. Could I do this with an upgrade disc or would I need to buy the whole OS? I'm trying to avoid paying 200$ to activate Ultimate.

Yes - you can do a full install with an upgrade disk - hundreds of simple guides to the process available online - just google it. You should back up all your data and run a full disk format before the install.