No, the Bandit does not have a CDI, although some shops will tell you this. CDI ignitions require largish capacitors, looking at pictures of the Digitial Igniter box you'll realize it's nothing more than a simple computer.
There is a magnetic pickup coil that sends a signal to the Digital Igniter, the igniter then energizes the coils. In this case think of the pickup as a set of points and realize that the Digital Igniter is just there for solid-state timing advance and rev-limiting. Actually, it does more, since there is just one pickup for 4 cylinders. Not knowing the specifics I can only assume the signal from the pickup is different every 180 degrees or so, so that the igniter knows what coils to energize.
Oh, and I think the igniter also drives your Tachometer.