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

Fast decimal floating-point division

A new implementation for decimal floating-point (DFP) division is introduced. The algorithm is based on high-radix SRT division The SRT division algorithm is named after D. Sweeney, J. E. Robertson, and T. D. Tocher. with the recurrence in a new decimal signed-digit format. Quotient digits are selected using comparison multiples, where the magnitude of the quotient digit is calculated by comparing the truncated partial remainder with limited precision multiples of the divisor. The sign is determined concurrently by investigating the polarity of the truncated partial remainder. A timing evaluation using a logic synthesis shows a significant decrease in the division execution time in contrast with one of the fastest DFP dividers reported in the open literatureHooman Nikmehr, Braden Phillips and Cheng-Chew Li

Study of Recursive Divide Architectures and Implementation for Division and Multiplication

Multipliers have been key and critical components for most application-specific and general-purpose computer architectures. However, these architectures have been transitioning towards multiple cores that can process large amounts of data through parallel approaches to computation. Unfortunately, traditional arithmetic functional units that worked well for single-core architectures have the side effect of incurring large amounts of area and power. Consequently, multi-core architecture need new ways of thinking about increased throughput to handle large amounts of data. This work discusses implementation of different divider algorithms and presents a recursive high radix divide unit that is modified to handle both multiplication and division targeted at multi-core architectures. Results are obtained with a 65nm technology and show a significant decrease in area and power while still maintaining a low total latency by utilizing high radix encoding within the functional unit.School of Electrical & Computer Engineerin

Generic low power reconfigurable distributed arithmetic processor

Higher performance, lower cost, increasingly minimizing integrated circuit components, and higher packaging density of chips are ongoing goals of the microelectronic and computer industry. As these goals are being achieved, however, power consumption and flexibility are increasingly becoming bottlenecks that need to be addressed with the new technology in Very Large-Scale Integrated (VLSI) design. For modern systems, more energy is required to support the powerful computational capability which accords with the increasing requirements, and these requirements cause the change of standards not only in audio and video broadcasting but also in communication such as wireless connection and network protocols. Powerful flexibility and low consumption are repellent, but their combination in one system is the ultimate goal of designers. A generic domain-specific low-power reconfigurable processor for the distributed arithmetic algorithm is presented in this dissertation. This domain reconfigurable processor features high efficiency in terms of area, power and delay, which approaches the performance of an ASIC design, while retaining the flexibility of programmable platforms. The architecture not only supports typical distributed arithmetic algorithms which can be found in most still picture compression standards and video conferencing standards, but also offers implementation ability for other distributed arithmetic algorithms found in digital signal processing, telecommunication protocols and automatic control. In this processor, a simple reconfigurable low power control unit is implemented with good performance in area, power and timing. The generic characteristic of the architecture makes it applicable for any small and medium size finite state machines which can be used as control units to implement complex system behaviour and can be found in almost all engineering disciplines. Furthermore, to map target applications efficiently onto the proposed architecture, a new algorithm is introduced for searching for the best common sharing terms set and it keeps the area and power consumption of the implementation at low level. The software implementation of this algorithm is presented, which can be used not only for the proposed architecture in this dissertation but also for all the implementations with adder-based distributed arithmetic algorithms. In addition, some low power design techniques are applied in the architecture, such as unsymmetrical design style including unsymmetrical interconnection arranging, unsymmetrical PTBs selection and unsymmetrical mapping basic computing units. All these design techniques achieve extraordinary power consumption saving. It is believed that they can be extended to more low power designs and architectures. The processor presented in this dissertation can be used to implement complex, high performance distributed arithmetic algorithms for communication and image processing applications with low cost in area and power compared with the traditional methods

Introduction to Logic Circuits & Logic Design with VHDL

The overall goal of this book is to fill a void that has appeared in the instruction of digital circuits over the past decade due to the rapid abstraction of system design. Up until the mid-1980s, digital circuits were designed using classical techniques. Classical techniques relied heavily on manual design practices for the synthesis, minimization, and interfacing of digital systems. Corresponding to this design style, academic textbooks were developed that taught classical digital design techniques. Around 1990, large-scale digital systems began being designed using hardware description languages (HDL) and automated synthesis tools. Broad-scale adoption of this modern design approach spread through the industry during this decade. Around 2000, hardware description languages and the modern digital design approach began to be taught in universities, mainly at the senior and graduate level. There were a variety of reasons that the modern digital design approach did not penetrate the lower levels of academia during this time. First, the design and simulation tools were difficult to use and overwhelmed freshman and sophomore students. Second, the ability to implement the designs in a laboratory setting was infeasible. The modern design tools at the time were targeted at custom integrated circuits, which are cost- and time-prohibitive to implement in a university setting. Between 2000 and 2005, rapid advances in programmable logic and design tools allowed the modern digital design approach to be implemented in a university setting, even in lower-level courses. This allowed students to learn the modern design approach based on HDLs and prototype their designs in real hardware, mainly field programmable gate arrays (FPGAs). This spurred an abundance of textbooks to be authored teaching hardware description languages and higher levels of design abstraction. This trend has continued until today. While abstraction is a critical tool for engineering design, the rapid movement toward teaching only the modern digital design techniques has left a void for freshman- and sophomore-level courses in digital circuitry. Legacy textbooks that teach the classical design approach are outdated and do not contain sufficient coverage of HDLs to prepare the students for follow-on classes. Newer textbooks that teach the modern digital design approach move immediately into high-level behavioral modeling with minimal or no coverage of the underlying hardware used to implement the systems. As a result, students are not being provided the resources to understand the fundamental hardware theory that lies beneath the modern abstraction such as interfacing, gate-level implementation, and technology optimization. Students moving too rapidly into high levels of abstraction have little understanding of what is going on when they click the “compile and synthesize” button of their design tool. This leads to graduates who can model a breadth of different systems in an HDL but have no depth into how the system is implemented in hardware. This becomes problematic when an issue arises in a real design and there is no foundational knowledge for the students to fall back on in order to debug the problem

Automated Quantum Oracle Synthesis with a Minimal Number of Qubits

Several prominent quantum computing algorithms--including Grover's search algorithm and Shor's algorithm for finding the prime factorization of an integer--employ subcircuits termed 'oracles' that embed a specific instance of a mathematical function into a corresponding bijective function that is then realized as a quantum circuit representation. Designing oracles, and particularly, designing them to be optimized for a particular use case, can be a non-trivial task. For example, the challenge of implementing quantum circuits in the current era of NISQ-based quantum computers generally dictates that they should be designed with a minimal number of qubits, as larger qubit counts increase the likelihood that computations will fail due to one or more of the qubits decohering. However, some quantum circuits require that function domain values be preserved, which can preclude using the minimal number of qubits in the oracle circuit. Thus, quantum oracles must be designed with a particular application in mind. In this work, we present two methods for automatic quantum oracle synthesis. One of these methods uses a minimal number of qubits, while the other preserves the function domain values while also minimizing the overall required number of qubits. For each method, we describe known quantum circuit use cases, and illustrate implementation using an automated quantum compilation and optimization tool to synthesize oracles for a set of benchmark functions; we can then compare the methods with metrics including required qubit count and quantum circuit complexity.Comment: 18 pages, 10 figures, SPIE Defense + Commercial Sensing: Quantum Information Science, Sensing, and Computation X