Parallel additive implementation for modified FIRS

Many non-standard radix number representation systems have been proposed in order to speed up the computational time. The most famous system is the signed-digit number representation system of Avizienis. This is a redundancy system (i.e., at least one number can have more than one representation.) Redundancy property can be realized as a fast computation by using the parallel process. In this work, we consider a flexible interval representation system (FIRS) which can represent an interval as one sequence of digits. This paper proposes a solution for parallel additive operation together with the proof of correctness. Our work also includes a study of implementation in practical.