Recoders for Partial Compression and Rounding Recoders for Partial Compression and Rounding Recoders for Partial Compression and Rounding
نویسندگان
چکیده
The purpose of this paper is to treat digit set conversions and digit recodings in terms of primitive recoding operations that have elementary implementations. The partial compressions and roundings are each associated with borrow-save or carry-save recodings implementable in one level of logic. Iterative utilization of recoding have application for: i) reducing the range of truncated lower order digits of a redundant binary operand to intervals less than a 2 ulp range (?1; 1) approaching 1 ulp, ii) truncating strings of leading insigniicant digits in a redundant binary operand, iii) realizing Booth recoding for radices 2 k , k 2, by realizing the symmetric minimal redundant digit set for 2 k for all k bit substring of a redundant binary operand. Le but de ce travail est de traiter les conversions entre syst emes d' ecriture des nombres, et les conversions entre syst emes d' ecriture des chiires en termes d'op erations primitives de recodage qui poss edent une implantation el ementaire. La compression partielle et l'arrondi partiel associ es avec les syst emes de notation redondante borrow-save ou carry-save sont alors implant es en un seul niveau de cellules logiques. En utilisant plusieurs fois ces cellules de recodage, nous obtenons les applications suivantes : i) on peut r eduire le domaine de troncature des chiires de poids faible d'un nombre redondant a un intervalle plus petit que l'intervalle usuel ]?1; 11, jusqu'' a approcher un intervalle de largeur 1 ulp ; ii) on peut supprimer les chiires non signiicatifs de t^ ete d'un nombre redondant sans modiier sa valeur ; iii) le codage de Booth en base 2 k , k 2, est r ealis e en utilisant l'ensemble de chiires minimal sym etrique redondant pour 2 k a partir d'un nombre redondant quel-conque.
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