wuzzo
Premiere Elements 11 is compatible with Windows XP 32 bit SP3. But it will be a 32 bit application with all the resource limitations of a 32 bit system. I have not tried to install 11 on Windows XP 32 bit SP2. If you go by the published System Requirements for version 11, you see the "requirement" for the Windows XP SP3 included. No mention of SP2 for Windows XP.
What is the other computer operating system on which you want to install Premiere Elements 11? Only with Windows 7, 8, or 8.1 64 bit or Mac with 64 bit processor, Premiere Elements 11 will be a 64 bit application with all the resource perks of the 64 bit system.
Adobe allows you to run the same purchased serial number product on no more than 2 of your computers (and then not at the same time).
Please let us know if I have targeted your question. Please do not hesitate to ask questions or to ask for clarification.
ATR