Implementation alternatives for generalized signed-digit addition

Even though the theory of carry-free and limited-carry generalized signed-digit addition has been known for some time, exploration of the vast design space encompassing the number representation radix, choice of a redundant digit set, consideration of all possible encodings for operand and transfer digits, and selection of values for the various "free" parameters in the general algorithm has just begun. The authors review several implementation alternatives and place them into a unified framework that provides insight, facilitates comparisons and tradeoffs, helps future designers in effectively exploring the design space, and leads to novel representations or algorithms in some cases.<>