Fractions in the Canonical-Signed-Digit Number System

摘要

Canonical-signed-digit (CSD) coefficient representations lead to efficient add/subtract networks for hardwired DSP multiplies of two's complement signals. CSD has always been considered a fixed-point system, and available conversion algorithms operate on integers. Using methods applicable to many simple number systems, we rederive CSD for fractional numbers, derive a simple floating-point recursion for converting fractions to CSD, and briefly examine the associated truncation error.