Using existing TI2012 on older XP machine

I currently have TI2012 (a licensed version) running on my W7 PC. I am thinking of upgrading to TI 2013, but will I then be able to use the TI2012 on my old XP machine, or must I buy a new full license for TI2013?

If I do the later, will I be able to download a 32 bit version of TI2012 for my XP PC, (I assume that there are different installers for 32 and 64 bit), as the registered copy is for a 64 bit system? The functionality of 2012 is fine for my XP system.

What's the best (cheapest) way of getting to where I want to be?

David