New Formats for Computing with Real-Numbers under Round-to-Nearest

In this paper, a new family of formats to deal with real number for applications requiring round to nearest is proposed. They are based on shifting the set of exactly represented numbers which are used in conventional radix-beta number systems. This technique allows performing radix complement and round to nearest without carry propagation with negligible time and hardware cost. Furthermore, the proposed formats have the same storage cost and precision as standard ones. Since conversion to conventional formats simply require appending one extra-digit to the operands, standard circuits may be used to perform arithmetic operations with operands under the new format. We also extend the features of the RN-representation system and carry out a thorough comparison between both representation systems. We conclude that the proposed representation system is generally more adequate to implement systems for computation with real number under round-to-nearest.