Yes you can.
But keep a wheel barrow next to you with a lot of floppies. It is impossible nowadays to work without a hard drive. All this, to get rid of virus?
It is like burning the house to get rid of house bugs...!!
But, wait .... there is a solution. Buy an external harddrive that connects to your USB port. Periodically back up your harddrive inside your computer to this external one. This way, at least you are current upto the time you were hit with a virus. This is the only suggestion I can make and it is entirely do-able.
Or, you can back up your data files to a CD. You will need a CD writer. Blank CDs are cheap. So, throw the old one (punch a hole first) and keep only the new ones.
Another way: partition your hard drive. Always save your data in the second partition, so that, if you are hit by a virus only the system partition needs to be formatted and the operating system need to be reinstalled. Your data is still protected.
Nowadays some software allow you to automatically archive your data to a second partition - on a set day of the week at a set time. You do not have to even remember to do it, the software will do it for you.
For just $49, you can buy this one:
http://www.acronis.com
It is the best I have come across. It will also clone your hard drive to the external drive if you wish.
Good Luck.