On-line Digit Set Conversion for Rational Digit Number

Abstract

A number system that is well-designed can affect the computational time and the hardware implementation. An interesting number system called Round-to-Nearest coding (RN-coding) was proposed to reduce a time consuming in a rounding process. Rounding to the nearest in RN-coding can be done using only truncation at any positions in a sequence of digits (representation). This concept can save a lot of time in a parallel or pipeline computation manner. However, an RN-coding does not support an on-line arithmetic computation. In this paper, we propose a rational digit number system which is composed of rational signed-digits in the digit set. This new system preserves a round-to-nearest property and is suitable for an on-line arithmetic computation. Performing on-line elementary arithmetic operations in our system can be done by an on-line digit set conversion algorithm. We show that our new algorithm, which is an improvement of an on-line addition algorithm in our previous work, can be demonstrated by an on-line finite automaton with a finite on-line delay k.