Rational Digit Set for On-line Addition

Rounding process is one of the most important problems that limit an ability to perform a parallel or pipelining arithmetic computation in a computer system. An interesting number system called Round-to-Nearest coding (RN-coding) was proposed to solve those problems. A rounding process in an RN-coding can be done only by truncating at any position in a sequence of digits. However, an RN-coding is not suitable for on-line arithmetic operations. This paper proposes a new signeddigit number representation with a rational digit set. The obtained system also preserves a round-to-nearest property. We show in this work that an on-line addition can be illustrated as an on-line finite automaton with an on-line delay k.