{"title":"有理分数的模表示","authors":"S. A. Inyutin","doi":"10.17587/it.29.406-413","DOIUrl":null,"url":null,"abstract":"The computer is designed to perform calculations, therefore it is a device for automatically processing machine data formats that display structured information. In machine data formats, the digit grid of typical and specialized computers displays numerical values on which calculations are performed in various number systems. A new modular packed representation of numerical values by rational fractions with fixed denominators, previously unknown, is introduced. For such modular representations of numerical quantities, a basic algorithm for the formation of vector components of types of representations is given with an estimate of complexity. A method of optimal approximation by packed modular representations of arbitrary irregular fractions has been found. The features of algorithms for performing additive and multiplicative operations for packed representations in a modular processor are analyzed.","PeriodicalId":37476,"journal":{"name":"Radioelektronika, Nanosistemy, Informacionnye Tehnologii","volume":"32 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Modular Representation of Rational Fractions\",\"authors\":\"S. A. Inyutin\",\"doi\":\"10.17587/it.29.406-413\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The computer is designed to perform calculations, therefore it is a device for automatically processing machine data formats that display structured information. In machine data formats, the digit grid of typical and specialized computers displays numerical values on which calculations are performed in various number systems. A new modular packed representation of numerical values by rational fractions with fixed denominators, previously unknown, is introduced. For such modular representations of numerical quantities, a basic algorithm for the formation of vector components of types of representations is given with an estimate of complexity. A method of optimal approximation by packed modular representations of arbitrary irregular fractions has been found. The features of algorithms for performing additive and multiplicative operations for packed representations in a modular processor are analyzed.\",\"PeriodicalId\":37476,\"journal\":{\"name\":\"Radioelektronika, Nanosistemy, Informacionnye Tehnologii\",\"volume\":\"32 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-08-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Radioelektronika, Nanosistemy, Informacionnye Tehnologii\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17587/it.29.406-413\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Materials Science\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Radioelektronika, Nanosistemy, Informacionnye Tehnologii","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17587/it.29.406-413","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Materials Science","Score":null,"Total":0}
The computer is designed to perform calculations, therefore it is a device for automatically processing machine data formats that display structured information. In machine data formats, the digit grid of typical and specialized computers displays numerical values on which calculations are performed in various number systems. A new modular packed representation of numerical values by rational fractions with fixed denominators, previously unknown, is introduced. For such modular representations of numerical quantities, a basic algorithm for the formation of vector components of types of representations is given with an estimate of complexity. A method of optimal approximation by packed modular representations of arbitrary irregular fractions has been found. The features of algorithms for performing additive and multiplicative operations for packed representations in a modular processor are analyzed.
期刊介绍：
Journal “Radioelectronics. Nanosystems. Information Technologies” (abbr RENSIT) publishes original articles, reviews and brief reports, not previously published, on topical problems in radioelectronics (including biomedical) and fundamentals of information, nano- and biotechnologies and adjacent areas of physics and mathematics. The authors of the journal are academicians, corresponding members and foreign members of the Russian Academy of Natural Sciences (RANS) and their colleagues, as well as other russian and foreign authors on the proposal of the members of RANS, which can be obtained by the author before sending articles to the editor or after its arrival on the recommendation of a member of the editorial board or another member of the RANS, who gave the opinion on the article at the request of the editior. The editors will accept articles in both Russian and English languages. Articles are internally peer reviewed (double-blind peer review) by members of the Editorial Board. Some articles undergo external review, if necessary. Designed for researchers, graduate students, physics students of senior courses and teachers. It turns out 2 times a year (that includes 2 rooms)
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