High Speed Multiplier using High Accuracy Floating Point Logarithmic Number System

Abstract

The ASIC implementation of the high speed multiplier using high accuracy floating point logarithmic number system is reported in this paper. Most popularly used techniques to compute logarithmic calculations for digital signal processors are lookup table based implementation, polynomial approximation, and Taylor series expansion. But, all of these techniques suffer from low accuracy due to choice of only lower order terms of the expanded series. In the present work, logarithmic conversion is implemented by floating point (IEEE-754 single precision) converting methodology thereby eliminate series expansion which eventually resulted in high accuracy. The improvement in speed, by avoidance of carry propagation, was achieved through canonical signed digit code (CSDC) implementation, while the high accuracy was achieved through an error minimization circuitry specially designed for this purpose. The functionality of these circuits was checked and performance parameters like propagation delay and dynamic power consumption were calculated by spice spectre using 90nm CMOS technology. The propagation delay & power consumption of the resulting (128×128) bit multiplier (divider) was only ~93ns & ~80mW respectively for a layout area of ~25mm2. The implementation offered significant improvement in terms of accuracy, delay and power from earlier reported ones.