An Efficient Base Conversion Using Variable Length Segmentation and Remainder Transfer

Abstract

This letter addresses the problems of conversion overflows, losses, and faults in the radix number system. Different from the fixed length truncation conversion strategy, the proposed scheme determines the optimal length of each segment adaptively according to the bases of source and destination and the representable numbers range limited by the maximum storage capacity of registers. In the segmentation repeated division scheme, the term of segment weight is presented to reflect the influence of different segment positions on the size of corresponding segment value, and a remainder transfer function that can interrelate individual segments is established to correct the dividend automatically. Theoretical and experimental results prove that the proposed scheme can realize the defect-free radix conversion for any integers between any bases and improve conversion efficiency up to the theoretical value.