On arithmetic inter-relationships and hardware interchangeabiltty of negabinary and binary systems

Abstract

Recent use of the negabinary system in the application oriented digital hardware, has encouraged the search for suitable arithmetic algorithms in −2 base. These algorithms have been directly utilized in designing logic circuits and several logic implementations have been reported in the literature. The main objective of this paper is to show the close relationship between +2 base addition and −2 base negative addition. Two possible ways of utilizing binary adders for performing negabinary addition and their underlying theories are presented. Two similar techniques of using negabinary adders for binary addition are also considered in detail. An interesting aspect of this investigation about negabinary base is that negative addition (rather than just addition) seems to be the primitive operation from logic complexity and interchangeability of +2 and −2 adders point of view. The technique of adding two numbers in one system by the adders of the other system is extended here for multiple operand addition. This requires inclusion of an additional correction factor. Further, the additive algorithms of this work lead to four simple conversion processes of number from one system to another. This paper seems to be a realistic step towards the use of similar hardware for +2 and −2 bases and hence this allows an instantaneous flexibility on the selection of number system. It is believed that this paper will attract more attention on the use of −2 base system for the design of special purpose digital machines and process controllers.