  A formal description of a quantum abacus based encoding system is presented.
This way of representing data for processing purposes is based on a quantum
algorithm for counting qubits introduced by Lesovik et al.
\cite{LesovikEtal2010} and Suslov et al. \cite{SuslovEtal2011}, but formally
developed in this work. Finally, in order to illustrate the potential of this
proposal, the implementation of the basic quantum array operations through this
encoding system is presented.
