The Battlefield 4 sub-reddit has revealed that the Battlefield 4 Beta will require a 64-bit operating system to be able to run the game. I noticed myself last night that the name of the beta had x64 at the end of it.
A tweet earlier today by Johan Andersson, Technical Director on Frostbite at DICE, has now confirmed that you will indeed need an x64 operating system. Those of you that aren't on a 64-bit operating system by now are definitely out of luck, at least for the beta.
@GiGaB4yt the beta is only for 64-bit Windows as we have a native 64-bit executable— Johan Andersson (@repi) September 25, 2013
There is no confirmation as of yet as to whether or not the final build of the game will run on 32-bit machines, but if you're picking Battlefield 4 up on PC then I'd be very surprised if you don't have a 64-bit operating system by now, especially considering the system requirements for the newer games.
Thanks, Pixel Enemy