{"title":"镜子算术","authors":"Jean P. Chinal","doi":"10.1109/ARITH.1975.6156975","DOIUrl":null,"url":null,"abstract":"Mirror coding for signed numbers is defined \"by means pf a set of primitive powers of two {+2<sup>n</sup>, −2<sup>n−1</sup>, …−2°} where signs of the usual set used in 2's complement representation are reversed. Use of the mirror representation is shown as an alternate design approach and is illustrated \"by a special purpose adder design in mirror code, by an alternate proof of a basic property of sign-ed-digit arithmetic and as another interpretation of cells used in some array multipliers for signed numbers. Lastly, the concept is used to define a variable mode redundant coding, allowing simple sign-flipping without overflow.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"75 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1975-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mirror arithmetic\",\"authors\":\"Jean P. Chinal\",\"doi\":\"10.1109/ARITH.1975.6156975\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Mirror coding for signed numbers is defined \\\"by means pf a set of primitive powers of two {+2<sup>n</sup>, −2<sup>n−1</sup>, …−2°} where signs of the usual set used in 2's complement representation are reversed. Use of the mirror representation is shown as an alternate design approach and is illustrated \\\"by a special purpose adder design in mirror code, by an alternate proof of a basic property of sign-ed-digit arithmetic and as another interpretation of cells used in some array multipliers for signed numbers. Lastly, the concept is used to define a variable mode redundant coding, allowing simple sign-flipping without overflow.\",\"PeriodicalId\":360742,\"journal\":{\"name\":\"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)\",\"volume\":\"75 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1975-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ARITH.1975.6156975\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ARITH.1975.6156975","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Mirror coding for signed numbers is defined "by means pf a set of primitive powers of two {+2n, −2n−1, …−2°} where signs of the usual set used in 2's complement representation are reversed. Use of the mirror representation is shown as an alternate design approach and is illustrated "by a special purpose adder design in mirror code, by an alternate proof of a basic property of sign-ed-digit arithmetic and as another interpretation of cells used in some array multipliers for signed numbers. Lastly, the concept is used to define a variable mode redundant coding, allowing simple sign-flipping without overflow.
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