You can represent 0 by absence.

     : 0
  o  : 1
  oo : 2
  ooo: 3

Of course, this is not a practical notation, since 0 would hard to distinguish from actual absence, but it would be viable in some situations: a table of numbers say, where you know that no cells are empty. So theoretically, it is possible to represent 0 in base 1, regardless of its obvious impracticalities.