Digit-set Conversions: Generalizations and Applications

The problem of digit set conversion for xed 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 preex 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 here as exempliications.