Abstract: The carry-propagation-free addition which is independently of operand length is feasible only if the outputs are expressed in the redundant representations. Binary sign-digit and carry-save representations are the two popular redundant formats which are widely used in the implementation of high-speed multipliers. In the previous studies, these two representations are treated separately. In this study, the algorithms and implementations are proposed for the conversion between them, thus, the computer arithmetic developed for one representation can be easily adapted to the other. The conversion overheads in the area and speed are also discussed.