The implementation and applications of multiple-valued logic

Multiple-Valued Logic (MVL) takes two major forms. Multiple-valued circuits can implement the logic directly by using multiple-valued signals, or the logic can be implemented indirectly with binary circuits, by using more than one binary signal to represent a single multiple-valued signal. Techniques such as carry-save addition can be viewed as indirectly implemented MVL. Both direct and indirect techniques have been shown in the past to provide advantages over conventional arithmetic and logic techniques in algorithms required widely in computing for applications such as image and signal processing. It is possible to implement basic MVL building blocks at the transistor level. However, these circuits are difficult to design due to their non binary nature. In the design stage they are more like analogue circuits than binary circuits. Current integrated circuit technologies are biased towards binary circuitry. However, in spite of this, there is potential for power and area savings from MVL circuits, especially in technologies such as BiCMOS. This thesis shows that the use of voltage mode MVL will, in general not provide bandwidth increases on circuit buses because the buses become slower as the number of signal levels increases. Current mode MVL circuits however do have potential to reduce power and area requirements of arithmetic circuitry. The design of transistor level circuits is investigated in terms of a modern production technology. A novel methodology for the design of current mode MVL circuits is developed. The methodology is based upon the novel concept of the use of non-linear current encoding of signals, providing the opportunity for the efficient design of many previously unimplemented circuits in current mode MVL. This methodology is used to design a useful set of basic MVL building blocks, and fabrication results are reported. The creation of libraries of MVL circuits is also discussed. The CORDIC algorithm for two dimensional vector rotation is examined in detail as an example for indirect MVL implementation. The algorithm is extended to a set of three dimensional vector rotators using conventional arithmetic, redundant radix four arithmetic, and Taylor's series expansions. These algorithms can be used for two dimensional vector rotations in which no scale factor corrections are needed. The new algorithms are compared in terms of basic VLSI criteria against previously reported algorithms. A pipelined version of the redundant arithmetic algorithm is floorplanned and partially laid out to give indications of wiring overheads, and layout densities. An indirectly implemented MVL algorithm such as the CORDIC algorithm described in this thesis would clearly benefit from direct implementation in MVL

New Views for Stochastic Computing: From Time-Encoding to Deterministic Processing

University of Minnesota Ph.D. dissertation.July 2018. Major: Electrical/Computer Engineering. Advisor: David Lilja. 1 computer file (PDF); xi, 149 pages.Stochastic computing (SC), a paradigm first introduced in the 1960s, has received considerable attention in recent years as a potential paradigm for emerging technologies and ''post-CMOS'' computing. Logical computation is performed on random bitstreams where the signal value is encoded by the probability of obtaining a one versus a zero. This unconventional representation of data offers some intriguing advantages over conventional weighted binary. Implementing complex functions with simple hardware (e.g., multiplication using a single AND gate), tolerating soft errors (i.e., bit flips), and progressive precision are the primary advantages of SC. The obvious disadvantage, however, is latency. A stochastic representation is exponentially longer than conventional binary radix. Long latencies translate into high energy consumption, often higher than that of their binary counterpart. Generating bit streams is also costly. Factoring in the cost of the bit-stream generators, the overall hardware cost of an SC implementation is often comparable to a conventional binary implementation. This dissertation begins by proposing a highly unorthodox idea: performing computation with digital constructs on time-encoded analog signals. We introduce a new, energy-efficient, high-performance, and much less costly approach for SC using time-encoded pulse signals. We explore the design and implementation of arithmetic operations on time-encoded data and discuss the advantages, challenges, and potential applications. Experimental results on image processing applications show up to 99% performance speedup, 98% saving in energy dissipation, and 40% area reduction compared to prior stochastic implementations. We further introduce a low-cost approach for synthesizing sorting network circuits based on deterministic unary bit-streams. Synthesis results show more than 90% area and power savings compared to the costs of the conventional binary implementation. Time-based encoding of data is then exploited for fast and energy-efficient processing of data with the developed sorting circuits. Poor progressive precision is the main challenge with the recently developed deterministic methods of SC. We propose a high-quality down-sampling method which significantly improves the processing time and the energy consumption of these deterministic methods by pseudo-randomizing bitstreams. We also propose two novel deterministic methods of processing bitstreams by using low-discrepancy sequences. We further introduce a new advantage to SC paradigm-the skew tolerance of SC circuits. We exploit this advantage in developing polysynchronous clocking, a design strategy for optimizing the clock distribution network of SC systems. Finally, as the first study of its kind to the best of our knowledge, we rethink the memory system design for SC. We propose a seamless stochastic system, StochMem, which features analog memory to trade the energy and area overhead of data conversion for computation accuracy

Development of FPGA based Standalone Tunable Fuzzy Logic Controllers

Soft computing techniques differ from conventional (hard) computing, in that unlike hard computing, it is tolerant of imprecision, uncertainty, partial truth, and approximation. In effect, the role model for soft computing is the human mind and its ability to address day-to-day problems. The principal constituents of Soft Computing (SC) are Fuzzy Logic (FL), Evolutionary Computation (EC), Machine Learning (ML) and Artificial Neural Networks (ANNs). This thesis presents a generic hardware architecture for type-I and type-II standalone tunable Fuzzy Logic Controllers (FLCs) in Field Programmable Gate Array (FPGA). The designed FLC system can be remotely configured or tuned according to expert operated knowledge and deployed in different applications to replace traditional Proportional Integral Derivative (PID) controllers. This re-configurability is added as a feature to existing FLCs in literature. The FLC parameters which are needed for tuning purpose are mainly input range, output range, number of inputs, number of outputs, the parameters of the membership functions like slope and center points, and an If-Else rule base for the fuzzy inference process. Online tuning enables users to change these FLC parameters in real-time and eliminate repeated hardware programming whenever there is a need to change. Realization of these systems in real-time is difficult as the computational complexity increases exponentially with an increase in the number of inputs. Hence, the challenge lies in reducing the rule base significantly such that the inference time and the throughput time is perceivable for real-time applications. To achieve these objectives, Modified Rule Active 2 Overlap Membership Function (MRA2-OMF), Modified Rule Active 3 Overlap Membership Function (MRA3-OMF), Modified Rule Active 4 Overlap Membership Function (MRA4-OMF), and Genetic Algorithm (GA) base rule optimization methods are proposed and implemented. These methods reduce the effective rules without compromising system accuracy and improve the cycle time in terms of Fuzzy Logic Inferences Per Second (FLIPS). In the proposed system architecture, the FLC is segmented into three independent modules, fuzzifier, inference engine with rule base, and defuzzifier. Fuzzy systems employ fuzzifier to convert the real world crisp input into the fuzzy output. In type 2 fuzzy systems there are two fuzzifications happen simultaneously from upper and lower membership functions (UMF and LMF) with subtractions and divisions. Non-restoring, very high radix, and newton raphson approximation are most widely used division algorithms in hardware implementations. However, these prevalent methods have a cost of more latency. In order to overcome this problem, a successive approximation division algorithm based type 2 fuzzifier is introduced. It has been observed that successive approximation based fuzzifier computation is faster than the other type 2 fuzzifier. A hardware-software co-design is established on Virtex 5 LX110T FPGA board. The MATLAB Graphical User Interface (GUI) acquires the fuzzy (type 1 or type 2) parameters from users and a Universal Asynchronous Receiver/Transmitter (UART) is dedicated to data communication between the hardware and the fuzzy toolbox. This GUI is provided to initiate control, input, rule transfer, and then to observe the crisp output on the computer. A proposed method which can support canonical fuzzy IF-THEN rules, which includes special cases of the fuzzy rule base is included in Digital Fuzzy Logic Controller (DFLC) architecture. For this purpose, a mealy state machine is incorporated into the design. The proposed FLCs are implemented on Xilinx Virtex-5 LX110T. DFLC peripheral integration with Micro-Blaze (MB) processor through Processor Logic Bus (PLB) is established for Intellectual Property (IP) core validation. The performance of the proposed systems are compared to Fuzzy Toolbox of MATLAB. Analysis of these designs is carried out by using Hardware-In-Loop (HIL) test to control various plant models in MATLAB/Simulink environments