Issue No. 05 - May (1994 vol. 43)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.280811
<p>The problem of digit set conversion for fixed radix is investigated for the case of converting into a non redundant, as well as into a redundant, digit set. Conversion may be from very general digit sets, and covers as special cases multiplier recodings, additions, and certain multiplications. We generalize known algorithms for conversions into non redundant digit sets, as well as apply conversion to generalize the O(log n) time algorithm for conditional sum addition using parallel prefix computation, and a comparison is made with standard carry-lookahead techniques. Examples on multi-operand addition are used to illustrate the generality of this approach. O(1) time algorithms for converting into redundant digit sets are generalized based on a very simple lemma, which provides a framework for all conversions into redundant digit sets. Applications in multiplier recoding and partial product accumulation are used as exemplifications.</p>
digital arithmetic; multiplying circuits; computer arithmetic; conditional sum addition; digit set conversion; multiplier recoding; redundant representation; nonredundant representation; on-the-fly conversion; parallel prefix computation; carry-lookahead techniques.
P. Kornerup, "Digit-Set Conversions: Generalizations and Applications", IEEE Transactions on Computers, vol. 43, no. , pp. 622-629, May 1994, doi:10.1109/12.280811