Difficult operations in the multi-dimensional logarithmic number system.

Date of Award


Degree Type


Degree Name



Electrical and Computer Engineering

First Advisor

Jullien, G. A.


Engineering, Electronics and Electrical.




The Multi-Dimensional Logarithmic Number System (MDLNS), with similar properties to the Logarithmic Number System (LNS), provides more degrees of freedom than the LNS by virtue of having two or more orthogonal bases and the ability to use multiple digits. Unlike the LNS there is no direct functional relationship between binary/floating point representation and the MDLNS representation. Traditionally look-up tables (LUTs) were used to move from the binary domain to the MDLNS domain. This method could be unrealistic for hardware implementation when large binary ranges or multiple digits were used. The lack of this direct relationship also complicated the addition and subtraction operations in MDLNS. Again LUTs were used to perform these operations but they could become unrealistically large when multiple digits or large index ranges were used. The work presented in this thesis describes efficient techniques for implementing difficult MDLNS operations such as binary to MDLNS conversion as well as addition and subtraction. These techniques require the use of a new memory device with range addressing capabilities, a RALUT (range addressable look-up table). The RALUT reduces the exponential complexity associated with the traditional use of potentially large LUTs by physically removing redundant hardware used to store the MDLNS conversion, addition, and subtraction information. Other significant MDLNS improvements such as choosing efficient and optimal bases, the one-bit sign architecture, and single-digit MDLNS RALUT reduction are also discussed. These improvements are shown to reduce the hardware implementation and improve performance without sacrificing any of the MDLNS accuracy.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2003 .M87. Source: Dissertation Abstracts International, Volume: 65-01, Section: B, page: 0365. Adviser: Graham Arnold Jullien. Thesis (Ph.D.)--University of Windsor (Canada), 2003.