A Generalized Multibit Recoding of Two's Complement Binary Numbers and its Proof with Application in Multiplier Implementations
Issue No. 08 - August (1990 vol. 39)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.57039
<p>A multibit recoding algorithm for signed two's complement binary numbers is presented and proved. In general, a k+1-bit recoding will result in a signed-digit (SD) representation of the binary number in radix 2/sup k/, using digits -2/sup k-1/ to +2/sup k-1/ including 0. It is shown that a correct SD representation of the original number is obtained by scanning K+1-tuples (k≤1) with one bit overlapping between adjacent groups. Recording of binary numbers has been used in computer arithmetic with 3-bit recoding being the dominant scheme. With the emergence of very high speed adders, hardware parallel multipliers using multibit recoding with k<2 are feasible, with the potential of improving both the performance and the hardware requirements. A parallel hardware multiplier based on the specific case of 5-bit recoding is proposed. Extensions beyond 5-bit recoding for multiplier design are studied for their performance and hardware requirements. Other issues relating to multiplier design, such as multiplication by a fixed or controlled coefficient, are also discussed in the light of multibit recoding.</p>
signed-digit representation; fixed coefficient multiplication; controlled coefficient multiplication; multibit recoding algorithm; signed two's complement binary numbers; radix 2/sup k/; computer arithmetic; very high speed adders; hardware parallel multipliers; 5-bit recoding; performance; digital arithmetic; multiplying circuits.
H. Sam and A. Gupta, "A Generalized Multibit Recoding of Two's Complement Binary Numbers and its Proof with Application in Multiplier Implementations," in IEEE Transactions on Computers, vol. 39, no. , pp. 1006-1015, 1990.