Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Ralph Benhart Iverson. / M.S.

Issued also as a Ph.D. Thesis in the Dept. of Electrical Engineering, 1966. / Bibliography: p.56.

Field Programmable Gate Arrays (FPGAs) support the reconfigurable computing paradigm by providing an integrated circuit hardware platform that facilitates software like reconfigurability. The addition of an embedded microprocessor and peripherals to traditional FPGA Combinational Logic Blocks (CLBs) interleaved with interconnections has effectively resulted in a programmable system on-chip. FPGAs are used to support flexible implementations of Application Specific Integrated Circuit (ASIC) functions. Because FPGAs are reconfigurable, they often are used in place of ASICs during the cicuit design process. FPGAs are also used when only a small number of ICs are required: ASICs necessitate large manufacturing runs to be economically viable; for smaller runs the use of FPGAs is an economic alternative. Application domains of interest, such as intelligent guidance systems, medical devices, and sensors, often require low power, inexpensive calculation of trance- dental functions. COordinate Rotation DIgital Computer (CORDIC) is an iterative algorithm used to emmulate hardware expensive multipliers, such as Multiply/ACculmulate (MAC) units, with only shift and add operations. However, because CORDIC is a sequential algorithm, characterized as having the latency of a serial multiplier, techniques that speed up computational performance have many applications.To this end, three implementations of standard CORDIC, (i) unrolled hardwired, (ii) unrolled programmable, and (iii) rolled programmable, were implemented on four Xilinx FPGA families: Virtex-4, -5, and -6, and Spartan-6. Although hardwired unrolled was found to have the greatest speed at the expense of no runtime flexibility, and rolled programmable was found to have the greatest flexibility and lowest silicon area consumption at the expense of the longest propagation delay, improvements to CORDIC implementations were still sought. Three parallelized CORDIC techniques, P-CORDIC, Flat-CORDIC, and Para-CORDIC, were implemented on the same four FPGA families. P-CORDIC and Flat-CORDIC, were shown to have the lowest latency under various conditions; Para-CORDIC was found to perform well in deeply pipelined, high throughput circuits. Design rules for when to use standard versus precomputation CORDIC techniques are presented. To address the low power requirements of many applications of interest, the Unfolded Multiplexor-LRB (UMUX-LRB), patent held by Sima, et al, was analyzed in weak inversion across four transistor technology nodes (180nm, 130nm, 90nm, and 65nm). Previous was also expanded from strong inversion across 180nm, 130nm, and 90nm technology nodes to also include 65nm. The UMUX-LRB interconnection network is based upon the Xilinx commercial interconnection network. Therefore, this network (MUX-LRB), and another static circuit technique, CMOS-Transmission Gates (CMOS-TG), were profiled across all four technology nodes to provide a baseline of comparision. This analysis found the UMUX-LRB to have the smallest and most balanced rising and falling edge propagation delay, in addition to having the greatest reliability for temperature and process variation. / Graduate

Typescript. / Thesis (Ph. D.)--University of Hawaii at Manoa, 1974. / Bibliography: leaves [112]-114. / iv, 114 leaves

Thesis (M.S.)--Duquesne University, 2004. / Title from document title page. Abstract included in electronic submission form. Includes bibliographical references (p. 24-25) and index.

abstract: Threshold logic has long been studied as a means of achieving higher performance and lower power dissipation, providing improvements by condensing simple logic gates into more complex primitives, effectively reducing gate count, pipeline depth, and number of interconnects. This work proposes a new physical implementation of threshold logic, the threshold logic latch (TLL), which overcomes the difficulties observed in previous work, particularly with respect to gate reliability in the presence of noise and process variations. Simple but effective models were created to assess the delay, power, and noise margin of TLL gates for the purpose of determining the physical parameters and assignment of input signals that achieves the lowest delay subject to constraints on power and reliability. From these models, an optimized library of standard TLL cells was developed to supplement a commercial library of static CMOS gates. The new cells were then demonstrated on a number of automatically synthesized, placed, and routed designs. A two-stage 2's complement integer multiplier designed with CMOS and TLL gates utilized 19.5% less area, 28.0% less active power, and 61.5% less leakage power than an equivalent design with the same performance using only static CMOS gates. Additionally, a two-stage 32-instruction 4-way issue queue designed with CMOS and TLL gates utilized 30.6% less area, 31.0% less active power, and 58.9% less leakage power than an equivalent design with the same performance using only static CMOS gates. / Dissertation/Thesis / Ph.D. Computer Science 2010

abstract: Threshold logic has been studied by at least two independent group of researchers. One group of researchers studied threshold logic with the intention of building threshold logic circuits. The earliest research to this end was done in the 1960's. The major work at that time focused on studying mathematical properties of threshold logic as no efficient circuit implementations of threshold logic were available. Recently many post-CMOS (Complimentary Metal Oxide Semiconductor) technologies that implement threshold logic have been proposed along with efficient CMOS implementations. This has renewed the effort to develop efficient threshold logic design automation techniques. This work contributes to this ongoing effort. Another group studying threshold logic did so, because the building block of neural networks - the Perceptron, is identical to the threshold element implementing a threshold function. Neural networks are used for various purposes as data classifiers. This work contributes tangentially to this field by proposing new methods and techniques to study and analyze functions implemented by a Perceptron After completion of the Human Genome Project, it has become evident that most biological phenomenon is not caused by the action of single genes, but due to the complex interaction involving a system of genes. In recent times, the `systems approach' for the study of gene systems is gaining popularity. Many different theories from mathematics and computer science has been used for this purpose. Among the systems approaches, the Boolean logic gene model has emerged as the current most popular discrete gene model. This work proposes a new gene model based on threshold logic functions (which are a subset of Boolean logic functions). The biological relevance and utility of this model is argued illustrated by using it to model different in-vivo as well as in-silico gene systems. / Dissertation/Thesis / Ph.D. Computer Science 2012

Circuitos baseados em portas lógicas de limiar (threshold logic gates – TLG) vem sendo estudados como uma alternativa promissora em relação ao tradicional estilo lógico CMOS, baseado no operadores AND e OR, na construção de circuitos integrados digitais. TLGs são capazes de implementar funções Booleanas mais complexas em uma única porta lógica. Diversos novos dispositivos, candidatos a substituir o transistor MOS, não se comportam como chaves lógicas e são intrinsicamente mais adequados à implementação de TLGs. Exemplos desses dispositivos são os memristores, spintronica, diodos de tunelamento ressonante (RTD), autômatos celulares quânticos (QCA) e dispositivos de tunelamento de elétron único (SET). Para o desenvolvimento de um fluxo de projeto de circuitos integrados baseados em lógica threshold, duas etapas são fundamentais: (1) identificar se uma dada função Booleana corresponde a uma função lógica threshold (TLF), isto é, pode ser implementada em um único TLG e computar os pesos desse TLG; (2) se uma função não é identificada como TLF, outro método de síntese lógica deve construir uma rede de TLGs otimizada que implemente a função. Este trabalho propõe métodos para atacar cada um desses dois problemas, e os resultados superam os métodos do estado-da-arte. O método proposto para realizar a identificação de TLFs é o primeiro método heurístico capaz de identificar todas as funções de cinco e seis variáveis, além de identificar mais funções que os demais métodos existentes quando o número de variáveis aumenta. O método de síntese de redes de TLGs é capaz de sintetizar circuitos reduzindo o número de portas TLG utilizadas, bem como a profundidade lógica e o número de interconexões. Essa redução é demonstrada através da síntese dos circuitos de avaliação da MCNC em comparação com os métodos já propostos na literatura. Tais resultados devem impactar diretamente na área e desempenho do circuito. / In this work, a novel method to synthesize digital integrated circuits (ICs) based on threshold logic gates (TLG) is proposed. Synthesis considering TLGs is quite relevant, since threshold logic has been revisited as a promising alternative to conventional CMOS IC design due to its suitability to emerging technologies, such as resonant tunneling diodes, memristors and spintronics devices. Identification and synthesis of threshold logic functions (TLF) are fundamental steps for the development of an IC design flow based on threshold logic. The first contribution is a heuristic algorithm to identify if a function can be implemented as a single TLG. Furthermore, if a function is not detected as a TLF, the method uses the functional composition approach to generate an optimized TLG network that implements the target function. The identification method is able to assign optimal variable weights and optimal threshold value to implement the function. It is the first heuristic algorithm that is not based on integer linear programming (ILP) that is able to identify all threshold functions with up to six variables. Moreover, it also identifies more functions than other related heuristic methods when the number of variables is more than six. Differently from ILP based approaches, the proposed algorithm is scalable. The average execution time is less than 1 ms per function. The second major contribution is the constructive process applied to generate optimized TLG networks taking into account multiple goals and design costs, like gate count, logic depth and number of interconnections. Experiments carried out over MCNC benchmark circuits show an average gate count reduction of 32%, reaching up to 54% of reduction in some cases, when compared to related approaches.

The memristor is an emerging nano-device. Low power operation, high density, scalability, non-volatility, and compatibility with CMOS Technology have made it a promising technology for memory, Boolean implementation, computing, and logic systems. This dissertation focuses on testing and design of such applications. In particular, we investigate on testing of memristor-based memories, design of memristive implementation of Boolean functions, and reliability and design of neuromorphic computing such as neural network. In addition, we show how to modify threshold logic gates to implement more functions. Although memristor is a promising emerging technology but is prone to defects due to uncertainties in nanoscale fabrication. Fast March tests are proposed in Chapter 2 that benefit from fast write operations. The test application time is reduced significantly while simultaneously reducing the average test energy per cell. Experimental evaluation in 45 nm technology show a speed-up of approximately 70% with a decrease in energy by approximately 40%. DfT schemes are proposed to implement the new test methods. In Chapter 3, an Integer Linear Programming based framework to identify current-mode threshold logic functions is presented. It is shown that threshold logic functions can be implemented in CMOS-based current mode logic with reduced transistor count when the input weights are not restricted to be integers. Experimental results show that many more functions can be implemented with predetermined hardware overhead, and the hardware requirement of a large percentage of existing threshold functions is reduced when comparing to the traditional CMOS-based threshold logic implementation. In Chapter 4, a new method to implement threshold logic functions using memristors is presented. This method benefits from the high range of memristor’s resistivity which is used to define different weight values, and reduces significantly the transistor count. The proposed approach implements many more functions as threshold logic gates when comparing to existing implementations. Experimental results in 45 nm technology show that the proposed memristive approach implements threshold logic gates with less area and power consumption. Finally, Chapter 5 focuses on current-based designs for neural networks. CMOS aging impacts the total synaptic current and this impacts the accuracy. Chapter 5 introduces an enhanced memristive crossbar array (MCA) based analog neural network architecture to improve reliability due to the aging effect. A built-in current-based calibration circuit is introduced to restore the total synaptic current. The calibration circuit is a current sensor that receives the ideal reference current for non-aged column and restores the reduced sensed current at each column to the ideal value. Experimental results show that the proposed approach restores the currents with less than 1% precision, and the area overhead is negligible.

abstract: Improving energy efficiency has always been the prime objective of the custom and automated digital circuit design techniques. As a result, a multitude of methods to reduce power without sacrificing performance have been proposed. However, as the field of design automation has matured over the last few decades, there have been no new automated design techniques, that can provide considerable improvements in circuit power, leakage and area. Although emerging nano-devices are expected to replace the existing MOSFET devices, they are far from being as mature as semiconductor devices and their full potential and promises are many years away from being practical. The research described in this dissertation consists of four main parts. First is a new circuit architecture of a differential threshold logic flipflop called PNAND. The PNAND gate is an edge-triggered multi-input sequential cell whose next state function is a threshold function of its inputs. Second a new approach, called hybridization, that replaces flipflops and parts of their logic cones with PNAND cells is described. The resulting \hybrid circuit, which consists of conventional logic cells and PNANDs, is shown to have significantly less power consumption, smaller area, less standby power and less power variation. Third, a new architecture of a field programmable array, called field programmable threshold logic array (FPTLA), in which the standard lookup table (LUT) is replaced by a PNAND is described. The FPTLA is shown to have as much as 50% lower energy-delay product compared to conventional FPGA using well known FPGA modeling tool called VPR. Fourth, a novel clock skewing technique that makes use of the completion detection feature of the differential mode flipflops is described. This clock skewing method improves the area and power of the ASIC circuits by increasing slack on timing paths. An additional advantage of this method is the elimination of hold time violation on given short paths. Several circuit design methodologies such as retiming and asynchronous circuit design can use the proposed threshold logic gate effectively. Therefore, the use of threshold logic flipflops in conventional design methodologies opens new avenues of research towards more energy-efficient circuits. / Dissertation/Thesis / Doctoral Dissertation Computer Science 2015