Performance evaluation of the canonical signed-digit code (CSC)
M. Peard, D. Esteban · 2005
This paper discusses algorithms and performance, in terms of average number of operative symbols for shift right and shift left Canonical Signed-digit Codes [CSC] which can be applied to generation of multiplications on sequential type microprocessing machines. The reference algorithms are based on application of codes which minimize the number of operative symbols required to perform binary multiplications by introducing a canonical form based on the use of +1, -1 symbols. For instance, the binary representation of the signed number 7 which is written 0 1 1 1 in a 2's complement Natural Binary Code [NBC] is represented by 1 0 0 -1 in the CSC form. The paper will assess the following points :\bulletSynthesis and properties of CSC for truncated multiplications (shift right algorithm) or non-truncated multiplications (shift left algorithm),\bulletComparison of the relative number of operative symbols required by a CSC and a NBC,\bulletEvaluation of the average number of operative symbols needed to code\Sin Xand(\Sin X)/Xwaveforms and for Gaussian or Gamma amplitude distributions.