Novel arithmetic implementations using cellular neural network arrays.

The primary goal of this research is to explore the use of arrays of analog self-synchronized cells---the cellular neural network (CNN) paradigm---in the implementation of novel digital arithmetic architectures. In exploring this paradigm we also discover that the implementation of these CNN arrays produces very low system noise; that is, noise generated by the rapid switching of current through power supply die connections---so called di/dt noise. With the migration to sub 100 nanometer process technology, signal integrity is becoming a critical issue when integrating analog and digital components onto the same chip, and so the CNN architectural paradigm offers a potential solution to this problem. A typical example is the replacement of conventional digital circuitry adjacent to sensitive bio-sensors in a SoC Bio-Platform. The focus of this research is therefore to discover novel approaches to building low-noise digital arithmetic circuits using analog cellular neural networks, essentially implementing asynchronous digital logic but with the same circuit components as used in analog circuit design. We address our exploration by first improving upon previous research into CNN binary arithmetic arrays. The second phase of our research introduces a logical extension of the binary arithmetic method to implement binary signed-digit (BSD) arithmetic. To this end, a new class of CNNs that has three stable states is introduced, and is used to implement arithmetic circuits that use binary inputs and outputs but internally uses the BSD number representation. Finally, we develop CNN arrays for a 2-dimensional number representation (the Double-base Number System - DBNS). A novel adder architecture is described in detail, that performs the addition as well as reducing the representation for further processing; the design incorporates an innovative self-programmable array. Extensive simulations have shown that our new architectures can reduce system noise by almost 70dB and crosstalk by more than 23dB over standard digital implementations.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2005 .I27. Source: Dissertation Abstracts International, Volume: 66-11, Section: B, page: 6159. Thesis (Ph.D.)--University of Windsor (Canada), 2005

Optimization Algorithms For The Multiple Constant Multiplications Problem

(Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2009(PhD) -- İstanbul Technical University, Institute of Science and Technology, 2009Bu tezde, birden fazla katsayının çarpımı (MCM) problemi, bir başka deyişle, bir değişkenin birden fazla katsayı ile çarpımının minimum sayıda toplama/çıkarma işlemi kullanılarak gerçeklenmesi için tasarlanmış kesin ve yaklaşık algoritmalar sunulmaktadır. Bir kesin alt ifade eliminasyonu (CSE) algoritmasının tasarımında, MCM problemini bir 0-1 tamsayı lineer programlama problemi olarak modelleyen daha önceden önerilmiş bir algoritma temel alınmıştır. Kesin CSE algoritması içinde, alan ve gecikme ölçütlerini ele alabilmek için yeni bir kesin model önerilmektedir. Kesin CSE algoritması tarafından taranacak arama uzayını küçültmek için problem indirgeme ve model basitleştirme teknikleri sunulmaktadır. Bu tekniklerin kullanımının kesin CSE algoritmasının daha büyük örnekler üzerinde uygulanmasına olanak sağladığı gösterilmektedir. Ayrıca, bu teknikler ile donatılmış kesin CSE algoritması, katsayıları genel sayı gösteriminde ele alacak ve kesin CSE algoritmasından daha iyi sonuçlar elde edecek şekilde genişletilmektedir. Bunların yanında, gerçek boyutlu örnekler üzerinde uygulanabilen bir kesin graf tabanlı algoritma sunulmaktadır. Bu kesin algoritmalara ek olarak, minimum sonuçlara oldukça yakın çözümler bulabilen ve kesin algoritmaların ele almakta zorlandığı örneklere uygulanabilen yaklaşık CSE ve graf tabanlı algoritmalar verilmektedir. Bu tezde önerilen kesin ve yaklaşık algoritmaların daha önceden önerilmiş sezgisel yöntemlerden daha iyi sonuçlar verdiği gösterilmektedir. Bunların yanısıra, bu tezde, kesin CSE algoritması gecikme kısıtı altında alanın minimize edilmesi, kapı seviyesinde alanın minimize edilmesi ve yüksek hızlı sayısal sonlu impuls cevaplı filtrelerin tasarımında alanın optimize edilmesi problemlerine uygulanmaktadır.In this thesis, exact and approximate algorithms designed for the multiple constant multiplications (MCM) problem, i.e., the implementation of the multiplication of a variable with multiple constants using minimum number of addition/subtraction operations, are introduced. In the design of an exact common subexpression elimination (CSE) algorithm, we relied on the previously proposed algorithm that models the MCM problem as a 0-1 integer linear programming problem. To handle the area and delay parameters in the exact CSE algorithm, a new exact model is proposed. To reduce the search space to be explored by the exact algorithm, problem reduction and model simplification techniques are introduced. It is shown that the use of these techniques enable the exact CSE algorithm to be applied on larger size instances. Also, the exact CSE algorithm equipped with these techniques is extended to handle the constants under general number representation yielding better solutions than those of the exact CSE algorithm. Besides, an exact graph-based algorithm that can be applied on real size instances is introduced. In addition to the exact algorithms, approximate CSE and graph-based algorithms that find similar results with the minimum solutions and can be applied on instances that the exact algorithms cannot deal with are presented. It is shown that the exact and approximate algorithms proposed in this thesis give better solutions than those of the previously proposed heuristic algorithms. Furthermore, in this thesis, the exact CSE algorithm is applied on the minimization of area under a delay constraint, the minimization of area at gate-level, and the optimization of area in high-speed digital finite impulse response filters synthesis problems.DoktoraPh