Comments on "A carry-free 54 b×54 b multiplier using equivalent bit conversion algorithm"
M.D. Ercegovac, Thomas A. Lang, Yongjik Kim, B.-S. Song, John Grosspietsch, S.F. Gillig · IEEE Journal of Solid-State Circuits · 2003
For original paper see ibid., vol. 36, no. 10, p. 1538-1545 (Oct. 2001). In the aforementioned paper by Kim et al., a multiplier is presented which produces the result in radix-2 signed-digit representation. It is claimed that this representation can be converted into conventional magnitude representation by an algorithm which has no carry propagation. To the commenters this algorithm seems incorrect. The critical situation is a string which consists of a sequence of zeros followed by a -1; in such a case a carry is needed and the algorithm proposed is deemed incorrect. Consequently, it is pointed out that the proposed algorithm produces a correct multiplication result in conventional magnitude representation only if the signed-digit string does not have a sequence of 0's followed by a -1. The commenters show a multiplication example using the proposed conversion algorithm in which this situation occurs.