As others have said, a 64bit system is really the only way to address a full 4GB of memory and anything about 4GB of memory.
Whether you can run it depends upon a few things
#1). Your CPU must support it. But this support has been around for well over 5 years now
#2). Your hardware needs a 64bit driver
. Thus if you have an older printer, and it doesn't have a 64bit driver, you would be stuck with getting a new printer or using 64bit
#3). Your software will run on 64bit. Almost all 32bit software will work just fine...as of course would 64bit software. However, if you have any old 16bit software, this does NOT work under 64bit. This old software needs a 32bit OS which can also run 16bit.