Graduation Year

2005

Document Type

Thesis

Degree

M.S.Cp.E.

Degree Granting Department

Computer Engineering

Major Professor

N. Ranganathan, Ph.D.

Committee Member

Soontae Kim, Ph.D.

Committee Member

Justin E. Harlow III, M.S.

Keywords

Logarithmic number systems, Digital signal processing, Mitchell's algorithm, Convolution, Average error percentage

Abstract

The arithmetic operations such as multiplication and division in binary number system are computationally complex in terms of area, delay and power. Logarithmic Number Systems (LNS) offer a viable alternative combining the simplicity of fixed point number systems and the precision of floating point number systems. However, the computations in LNS result in some loss of accuracy and thus, are limited to mostly signal processing applications; where in certain amount of error is tolerable. In LNS, the cost of computations can be tradeoff with the level of accuracy needed. The Mitchell algorithm proposed incite[mitchell], is a simple approach commonly used for logarithmic multiplication. The method involves a high error margin due to a piecewise straight line approximation of the logarithm curve. Thus, several methods have been proposed in the literature for improving the accuracy of Mitchell's algorithm.

In this thesis, we propose a new method for improving the accuracy of Mitchell's logarithmic multiplication using operand decomposition. The operand decomposition process decreases the number of bits with the value of '1' in the multiplicands and reduces the amount of approximation. The proposed method brings down the average error percentage of Mitchell's logarithmic multiplication by around 45%. It can be combined with previous methods to further improve the accuracy. Experimental results are presented to show that both the error range and the average error percentage can be significantly improved by using operand decomposition.

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