An Unified Framework for Verifying Reverse Conversion Algorithms for Signed – Digit Number Systems - Chakraborty, MS; Ghosh, T; Mondal, AC (International Journal of Computer Sciences and Engineering, 2025)
For signed–digit number systems, the proof of correctness of some reverse conversion algorithms remain ingrained in their developmental methods. As far as the remaining reverse conversion algorithms are concerned, either of no formal proof is given or different verification techniques are followed. Consequently at some points of time even some faulty algorithms were proposed through recognized platforms and sought to be projected as breakthroughs. In this paper, it is shown that a majority of available reverse conversion algorithms may be directly verified in generic form in a concise manner, merely using an ordinary mathematical induction technique, guided by the fundamental rules of typical reverse conversion. In addition to that, as evident from the case study which is presented in this paper, both the verification process and outcomes of reverse conversion, using the former class of algorithms, may be easily used to scrutinize the other more complex reverse conversion algorithms. Thus a unified framework for verifying reverse conversion algorithms for signed – digit number systems might have been obtained.