A Collection of Contemporary Research Articles in Electronics, Communication & Computation- Book ISBN- 978-81-948050-7-6

Author: Dr. Madhu Sudan Chakraborty

Abstract: Signed-Digit Number Systems have been resurging as a potential contender of the conventional radix-complement number system. However, even at the present level of technical advancement, the signed-digit number systems cannot cater to all computational needs. The ordinary signed-digit output of the common signed-digit arithmetic operations is to be transformed back into the conventional radix-complement form for further processing. This transformation is called the reverse conversion, and owing to consumption of significant delay, area and power overheads, it is often projected a major performance bottleneck of the signed-digit arithmetic. Even the subsequent radix-complement to sign-magnitude conversion, whenever needed, also attracts similar high overheads. Recently, Chakraborty and Mondal proposed a generic method for the constant-time conversion of the radix-complement output of signed-digit arithmetic operations into the sign-magnitude form with low overheads in order to counteract the high overheads of the reverse conversion as a whole. However, the Chakraborty-Mondal method has been proposed with abstract, generic terms. As the binary signed-digit number system has been being subjected to the most rigorous investigations among the various classes of signed-digit number systems on various issues, in this paper, the arithmetic constructs of the Chakraborty and Mondal algorithm is strived to be elaborated in sufficient details for the binary signed-digit number system, focusing its possible adaptation by the recent reverse conversion algorithm proposed by Sahoo, Gupta, Asati and Shekhar.

Keywords: Signed-digit number systems, Reverse conversion, Computer arithmetic, Constant-time conversion, Radix-complement to sign-magnitude transformation.