It's binary with the central dot/ding being the leading 1 and then toward the right

a ring is 0

a ring,ding is 1

The ring represents a doubling of its contents. The special case for the leading bit could be avoided by always having an innermost empty ring. That would also give you a better (i.e. visible) representation for 0. The addition rule ensures that you always have exactly 1 leading 0.