Recoders for partial compression and rounding.

Abstract

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 insignificant digits in a redundant binary operand, iii) realizing Booth recoding for radices 2k, k >= 2, by realizing the symmetric minimal redundant digit set for 2k for all k bit substring of a redundant binary operand.