Flexible interval representation system in negative binary base

Abstract

Interval arithmetic is widely used for handling uncertain data. Since an interval representation consists of one lower bound and one upper bound, they need more space usage and more computational time comparing to a traditional number representation. A Flexible Interval Representation System (FIRS) was introduced to deal with the problem. Space usage for FIRS can be reduced up to twenty-five percent. In this work, we propose a modified version of FIRS with respect to the negative binary base. The result shows that space can be reduced up to fifty percent. We also propose addition and subtraction algorithms together with a digit-set conversion using an on-the-fly conversion for this novel interval representation system.