The original Z64 had a hardware set limit of 128 Mbit. Because it was not capable of addressing any ram above 16MB, users could not open the system and change the Ram stick to a larger one and play bigger games. Once 256 Mbit games became more prevalent, the parent company released hardware version 2.0 which shipped with a 32MB ram chip and had the ability to address all 32MB of ram, allowing the larger games to play.
You can identify it by the serial number. The serial number of version 2 begins at 2, and 3 at three ( with the exception of the units sold over christmas '98) Also, when you turn on the Z64, it will read mr backup v2.11c, ( The numbers refer to the bios version, and the letter refers to the hardware version. a=1 b=2 c=3)
http://videogamedevelopmentdevices.wikia.com/wiki/Mr._Backup_Z64