Rational digit set for on-line addition

Thienprapasith, Pipop; Surarerks, Athasit

doi:10.1109/jcsse.2016.7748847

Cited by 1 publication

(3 citation statements)

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“…Example 1 A representation of = (312) 10 in a base = 3 with a digit set = {1 ̅ ,0, 1, 2}. Since the number of digits in the digit set is more than the base , it means that this system has a redundant property by Definition 2.…”

Section: Definition 1 (Conventional Number Representation)mentioning

confidence: 99%

“…Since the number of digits in the digit set is more than the base , it means that this system has a redundant property by Definition 2. Thus, the number = (312) 10 can have more than one representation in a base = 3 such as (111 ̅ 21 ̅ 0) 3 and (1101 ̅ 1 ̅ 0) 3 . □…”

Section: Definition 1 (Conventional Number Representation)mentioning

confidence: 99%

“…Since an elementary arithmetic operation can be expressed by a digit set conversion, we then propose an on-line digit set conversion algorithm that is demonstrated by an on-line finite automaton with an on-line delay in our system. This new algorithm is an improvement of an on-line addition algorithm in our previous work [10]. This paper is organized as follows: Section 2 recalls some background and notations used in this work.…”

Section: Introductionmentioning

confidence: 99%

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On-line Digit Set Conversion for Rational Digit Number

Thienprapasith¹,

Surarerks²

2017

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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 roundto-nearest property and is suitable for an on-line arithmetic computation. Performing online 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 .

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Section: Definition 1 (Conventional Number Representation)mentioning

confidence: 99%

Section: Definition 1 (Conventional Number Representation)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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