Improved algorithms and hardware designs for division by convergence

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Improved algorithms and hardware designs for division by convergence

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dc.contributor.advisor Swartzlander, Earl E.
dc.creator Kong, Inwook
dc.date.accessioned 2010-06-21T20:43:36Z
dc.date.available 2010-06-21T20:43:36Z
dc.date.created 2009-12
dc.date.issued 2010-06-21T20:43:36Z
dc.identifier.uri http://hdl.handle.net/2152/7844
dc.description.abstract This dissertation focuses on improving the division-by-convergence algorithm. While the division by convergence algorithm has many advantages, it has some drawbacks, such as a need for extra bits in the multiplier and a large ROM table for the initial approximation. To mitigate these problems, two new methods are proposed here. In addition, the research scope is extended to seek an efficient architecture for implementing a divider with Quantum-dot Cellular Automata (QCA), an emerging technology. For the first proposed approach, a new rounding method to reduce the required precision of the multiplier for division by convergence is presented. It allows twice the error tolerance of conventional methods and inclusive error bounds. The proposed method further reduces the required precision of the multiplier by considering the asymmetric error bounds of Goldschmidt dividers. The second proposed approach is a method to increase the speed of convergence for Goldschmidt division using simple logic circuits. The proposed method achieves nearly cubic convergence. It reduces the logic complexity and delay by using an approximate squarer with a simple logic implementation and a redundant binary Booth recoder. Finally, a new architecture for division-by-convergence in QCA is proposed. State machines for QCA often have synchronization problems due to the long wire delays. To resolve this problem, a data tag method is proposed. It also increases the throughput significantly since multiple division computations can be performed in a time skewed manner using one iterative divider.
dc.format.medium electronic
dc.language.iso eng
dc.rights Copyright © is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.
dc.subject Division-by-convergence
dc.subject Algorithms
dc.subject Quantum-dot Cellular Automata
dc.subject Synchronization
dc.subject Goldschmidt division
dc.title Improved algorithms and hardware designs for division by convergence
dc.description.department Electrical and Computer Engineering
dc.type.genre Thesis
dc.type.material text
thesis.degree.department Electrical and Computer Engineering
thesis.degree.discipline Electrical and Computer Engineering
thesis.degree.grantor The University of Texas at Austin
thesis.degree.level Doctoral
thesis.degree.name Doctor of Philosophy

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