Hardware Implementation of the Logarithm Function using Improved Parabolic Synthesis

Abstract: This thesis presents a design that approximates the fractional part of the based two logarithm function by using Improved Parabolic Synthesis including its CMOS VLSI implementations. Improved Parabolic Synthesis is a novel methodology in favor of implementing unary functions e.g. trigonometric, logarithm, square root etc. in hardware. It is an evolved approach from Parabolic Synthesis by combining it with Second-Degree Interpolation. In the thesis, the design explores a simple and parallel architecture for fast timing and optimizes wordlengths in computing stages for a small design. The error behavior of the design is described and char- acterized to meet the desired error metrics. This implementation is compared to other approaches e.g. Parabolic Synthesis and CORDIC using 65nm standard cell libraries and it is proved to have better performance in terms of smaller chip area, lower dynamic power, and shorter critical path.