An edited version of this work was accepted in IEEE Transactions on computers, DOI 10.1109/TC.2015.2479623In 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-R 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.Ministry of Education and Science of Spain under contracts TIN2013-42253-P
