
Yes, you can use one HDD but....
You will need to partition it so that Ubuntu has enough HDD space to move, that is why I suggested 20 GIG, but you could probably go down to 15 GIG, partitioned into 3.
But... if Win XP is using that part of that space, 16 Gig that you mention, as a a swap file, you will really have less than 16 GIG and more like 13 to 14. Also, when you format the Ubuntu partition will be losing some space as well.
Also, as RobLinux mentions some of the following above as well....
So, if you REallY want to get it to work now, I would suggest a deletion of all non-essential(or not used) programs in Win XP. Storage of all non-essential data to an external source(if you have a broadband connection, maybe you can store some of it on Google and Yahoo?). Of course, this would include deleting duplicate music, movies, or things you just don't need anymore. Then do a Complete Defrag and Scandisk. Then check your Swap Drive settings for Win XP, then you can really see if you have enough space for Ubuntu. This just takes time tidying up, but helps out tremendously when you want to dual boot!
I have installed both dual boot and stand alone of Ubuntu 6.06 LTS and 7.04 without a hitch on a Laptop with XP and desktops. The only main issue with Linux is that 'special' program that only runs on Windoz so a dual boot is one way to make sure everything works for you and then you can take the COMPLETE plunge!!!!

Hope that helps...!