Symbolic substitution basedcanonical recoding algorithms

Among the different algorithms that have been proposed for the conversion of a binary number to its canonical modified signed-digit representation, the Reitwiesnerʹs algorithm has been the most cited and regarded as the most efficient one in the computing literature. In this paper, however, we present two new conversion algorithms that are computationally more efficient than the Reitwiesnerʹs algorithm. Both of our algorithms use a lookup table and proceed using the symbolic substitution technique. An analysis of the computational efficiency of the proposed algorithms as determined by a computer simulation has also been presented.