{"title":"Intermediate variable encodings that enable multiplexor-based implementations of two operand addition","authors":"D. Phatak, I. Koren","doi":"10.1109/ARITH.1999.762824","DOIUrl":null,"url":null,"abstract":"In two operand addition, bit-wise intermediate variables such as the \"propagate\" and \"generate\" terms are defined/evaluated first. Basic carry propagation recursion is then expressed in terms of these variables and is \"unrolled\" to obtain a tree structure for fast execution. In CMOS VLSI technology, multiplexors are fast and efficient to implement. Hence, we investigate in this paper all possible two-bit encodings for the intermediate variables and identify the ones that enable multiplexor-based implementations. Some of these encodings enable further simplification of the multiplexor-based realizations. Our analysis also shows that adopting an intermediate signed-digit representation simply amounts to selecting one of the possible encodings. Thus, there is no inherent advantage to the use of intermediate signed-digit representations in a two operand addition. Finally, we extend our analysis to the generalized look-ahead-recursions proposed by R.W. Doran (1988).","PeriodicalId":434169,"journal":{"name":"Proceedings 14th IEEE Symposium on Computer Arithmetic (Cat. No.99CB36336)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1999-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","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.1999.762824","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
Abstract
In two operand addition, bit-wise intermediate variables such as the "propagate" and "generate" terms are defined/evaluated first. Basic carry propagation recursion is then expressed in terms of these variables and is "unrolled" to obtain a tree structure for fast execution. In CMOS VLSI technology, multiplexors are fast and efficient to implement. Hence, we investigate in this paper all possible two-bit encodings for the intermediate variables and identify the ones that enable multiplexor-based implementations. Some of these encodings enable further simplification of the multiplexor-based realizations. Our analysis also shows that adopting an intermediate signed-digit representation simply amounts to selecting one of the possible encodings. Thus, there is no inherent advantage to the use of intermediate signed-digit representations in a two operand addition. Finally, we extend our analysis to the generalized look-ahead-recursions proposed by R.W. Doran (1988).