  On the string of finite length, a (genomic) transposition is defined as the
operation of exchanging two consecutive substrings. The minimum number of
transpositions needed to transform one into the other is the transposition
distance, that has been researched in recent years. In this paper, we study
transposition distances on circular binary strings. A circular binary string is
the string that consists of symbols $0$ and $1$ and regards its circular shifts
as equivalent. The property of transpositions which partition strings is
observed. A lower bound on the transposition distance is represented in terms
of partitions. An upper bound on the transposition distance follows covering of
the set of partitions. The transposition diameter is given with a necessary and
sufficient condition.
