  In this paper, some issues concerning the Chinese remaindering representation
are discussed. Some new converting methods, including an efficient
probabilistic algorithm based on a recent result of von zur Gathen and
Shparlinski \cite{Gathen-Shparlinski}, are described. An efficient refinement
of the NC$^1$ division algorithm of Chiu, Davida and Litow
\cite{Chiu-Davida-Litow} is given, where the number of moduli is reduced by a
factor of $\log n$.
