Equivalence of reverse conversion of binary signed-digit number system and two's-complement to canonical signed-digit recording
Madhu Sudan Chakraborty, S. K. Sao, Arijit Mondal · 2018
For binary signed - digit arithmetic recording two's - complement numbers into canonical signed - digit form appears to be a performance bottleneck like reverse conversion. At the abstract level it seems that inverse operations are needed to record two's - complement number into canonical signed - digit form and to reverse convert binary signed - digit number system. However, in this article it is shown that a full - fledged computer arithmetic algorithm designed to solve one problem may be easily transformed for solving the other problem merely at some constant additional time. Accordingly, recording two's - complement numbers into canonical signed - digit form and reverse conversion of binary signed - digit number system may be treated as equivalent problem. Consequently all hardware architectures designed for either operation may be easily adapted to implement the other.