{"title":"并联、恒时转换和加法的充分必要条件","authors":"Peter Kornerup","doi":"10.1109/ARITH.1999.762840","DOIUrl":null,"url":null,"abstract":"This note presents necessary and sufficient conditions for parallel and constant time conversions from one digit-set into another, and thus also for constant time addition. In the integer domain it is generally believed that such conversion and addition is possible if the target digit-set is redundant and complete. This is also the case when the digit-set is a contiguous set of integers. However, when this is not the case then such conversion and addition in the integer domain is not possible in general, and when more general rings are considered, the same problem may be present.","PeriodicalId":434169,"journal":{"name":"Proceedings 14th IEEE Symposium on Computer Arithmetic (Cat. No.99CB36336)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1999-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"21","resultStr":"{\"title\":\"Necessary and sufficient conditions for parallel, constant time conversion and addition\",\"authors\":\"Peter Kornerup\",\"doi\":\"10.1109/ARITH.1999.762840\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This note presents necessary and sufficient conditions for parallel and constant time conversions from one digit-set into another, and thus also for constant time addition. In the integer domain it is generally believed that such conversion and addition is possible if the target digit-set is redundant and complete. This is also the case when the digit-set is a contiguous set of integers. However, when this is not the case then such conversion and addition in the integer domain is not possible in general, and when more general rings are considered, the same problem may be present.\",\"PeriodicalId\":434169,\"journal\":{\"name\":\"Proceedings 14th IEEE Symposium on Computer Arithmetic (Cat. No.99CB36336)\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1999-04-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"21\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings 14th IEEE Symposium on Computer Arithmetic (Cat. No.99CB36336)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ARITH.1999.762840\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings 14th IEEE Symposium on Computer Arithmetic (Cat. No.99CB36336)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ARITH.1999.762840","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Necessary and sufficient conditions for parallel, constant time conversion and addition
This note presents necessary and sufficient conditions for parallel and constant time conversions from one digit-set into another, and thus also for constant time addition. In the integer domain it is generally believed that such conversion and addition is possible if the target digit-set is redundant and complete. This is also the case when the digit-set is a contiguous set of integers. However, when this is not the case then such conversion and addition in the integer domain is not possible in general, and when more general rings are considered, the same problem may be present.
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