{"title":"非冗余剩余系统中的符号检测","authors":"Nicholas S. Szabó","doi":"10.1109/TEC.1962.5219388","DOIUrl":null,"url":null,"abstract":"The problem of sign determination in nonredundant residue systems is investigated. A general theorem is derived establishing necessary conditions for sign detection, and the use of this theorem is demonstrated through specific examples. It is shown that for a particular system organization these same conditions are also sufficient for sign detection. An implementation of this last system is presented for four moduli.","PeriodicalId":177496,"journal":{"name":"IRE Trans. Electron. Comput.","volume":"18 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1962-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"33","resultStr":"{\"title\":\"Sign Detection in Nonredundant Residue Systems\",\"authors\":\"Nicholas S. Szabó\",\"doi\":\"10.1109/TEC.1962.5219388\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The problem of sign determination in nonredundant residue systems is investigated. A general theorem is derived establishing necessary conditions for sign detection, and the use of this theorem is demonstrated through specific examples. It is shown that for a particular system organization these same conditions are also sufficient for sign detection. An implementation of this last system is presented for four moduli.\",\"PeriodicalId\":177496,\"journal\":{\"name\":\"IRE Trans. Electron. Comput.\",\"volume\":\"18 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1962-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"33\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IRE Trans. Electron. Comput.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/TEC.1962.5219388\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IRE Trans. Electron. Comput.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/TEC.1962.5219388","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The problem of sign determination in nonredundant residue systems is investigated. A general theorem is derived establishing necessary conditions for sign detection, and the use of this theorem is demonstrated through specific examples. It is shown that for a particular system organization these same conditions are also sufficient for sign detection. An implementation of this last system is presented for four moduli.