Signed Digit Representations of Minimal Hamming Weight
IEEE Transactions on Computers
The microarchitecture of the IBM eServer z900 processor
IBM Journal of Research and Development
Digital filter synthesis based on an algorithm to generate all minimal signed digit representations
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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Signed-power-of-two terms are widely used in design automation algorithms for digital filter synthesis and optimization, linear transformation and other multiple constant multiplication problems. In these applications, the computation efficiency or solution quality tends to degrade with the number of nonzero digits in the signed digit representation of the a priori fixed coefficients. This paper provides a new perspective to interpret the hamming weights of fixed-point coefficients represented in signed-power-of-two terms with minimal number of nonzero digits, called the minimal signed digit (MSD) representation. A new hamming weight pyramid (HWP) is proposed to succinctly compress the information about the distribution of the hamming weights of canonical signed digit (CSD) representation in a visually appealing manner for analysis and synthesis. CSD is a unique and popularly used subset of the general MSD representation. Many interesting properties of CSD are uncovered in this regularly structured HWP. These properties are exploited to develop a novel and elegant algorithm for the direct conversion of decimal number to CSD representation. We also show that the HWP can also be employed to overcome the limit imposed on the word length of the coefficients for the reduced adder graph (RAG) algorithm and filter coefficient synthesis.