How does a finite state machine perform division?

Question

I am taking a course on models of computation and currently we are doing finite state machines. One my tasks is to draw out a FSM that performs division of 3; to simplify the model the machine only accepts numbers multiple of 3. I am not sure how this exactly works, especially since I imagine FSM putting out only single binary values. Could you guys give examples (division by 2 or 4) or hints on how to approach this?

Answer 1

This is what you need, I think (sorry about the bad picture). The 'E' represents epsilon/lambda/no-output. The label of the edges denotes 'input/output'. For each symbol read there is also a corresponding output which may be lambda (no output).