Installing on new computer and keeping old one.

I am currently running Internet Security 2007 on an older HP desktop with Windows XP. This weekend I am buying a new HP computer with Windows 7 and a trial version of Norton installed. I plan to keep my old computer along with my new one, and wonder if I can use my subscription on both, since I have about eight months remaining. If so, what steps do I need to take? Also, both computers wil be using the same internet connection, via router, if that matters.