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Open Access Open Badges Research Article

Improving 2D-Log-Number-System Representations by Use of an Optimal Base

Roberto Muscedere

Author Affiliations

Electrical and Computer Engineering Department, University of Windsor, Windsor, ON, Canada, N9B3P4

EURASIP Journal on Advances in Signal Processing 2008, 2008:710590  doi:10.1155/2008/710590

The electronic version of this article is the complete one and can be found online at: http://asp.eurasipjournals.com/content/2008/1/710590

Received:10 April 2008
Accepted:20 June 2008
Published:25 June 2008

© 2008 The Author(s).

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The 2-dimensional logarithmic number system (2DLNS), a subset of the multi-DLNS (MDLNS), which has similar properties to the classical Logarithmic Number System (LNS), provides more degrees of freedom than the LNS by virtue of having two orthogonal bases and has the ability to use multiple 2DLNS components, or digits. The second base in 2DLNS can be adjusted to improve the representation space for particular applications; the difficulty is selecting such a base. This paper demonstrates how an optimal second base can considerably reduce the complexity of the system while significantly improving the representation space for application specific designs. The method presented here maps a specific set of numbers into the 2DLNS domain as efficiently as possible; a process that can be applied to any application. By moving from a two-bit sign to a one-bit sign, the computation time of the optimal base is halved, and the critical paths in existing architectures are reduced.

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