High performance, energy efficient logic style has always been a popular research topic in the field of very large scale integrated (VLSI) circuits because of the continuous demands of ever increasing circuit operating frequency. The invention of the dynamic logic in the 80s is one of the answers to this request as it allows designers to implement high performance circuit block, i.e., arithmetic logic unit (ALU), at an operating frequency that traditional static and pass transistor CMOS logic styles are difficult to achieve. However, the performance enhancement comes with several costs, including reduced noise margin,charge-sharing noise, and higher power dissipation due to higher data activity. Furthermore, dynamic logic has gradually lost its performance advantage over static logic due to the increased self-loading ratio in deep-submicron technology (65nm and below) because of the additional NMOS CLK footer transistor. Because of dynamic logic's limitations and diminished speed reward, a slowly rising need has emerged in the past decade to explore new logic style that goes beyond dynamic logic. In this thesis a constant delay (CD) logic style is proposed. The constant delay characteristic of this logic style regardless of the logic expression makes it suitable in implementing complicated logic expression such as addition. Moreover, CD logic exhibits a unique characteristic where the output is pre-evaluated before the inputs from the preceding stage is ready. This feature enables performance advantage over static and dynamic logic styles in a single cycle, multi-stage circuit block. Several design considerations including appropriate timing window width adjustment to reduce power consumption and maintain sufficient noise margin to ensure robust operations are discussed and analyzed. Using 65nm general purpose CMOS technology, the proposed logic demonstrates an average speed up of 94% and 56% over static and dynamic logic respectively in five different logic expressions. Post layout simulation results of 8-bit ripple carry adders conclude that CD-based design is 39% and 23% faster than the static and dynamic-based adders respectively. For ultra-high speed applications, CD-based design exhibits improved energy, power-delay product, and energy-delay product efficiency compared to static and dynamic counterparts.

This thesis includes two topics. The first topic is a low power design of 8-bit ANT-based pipelining CLA. The second one is a small digital to analog converter (DAC) used in an implantable neural stimulator. An ANT-based low-power 8-bit pipelining carry-lookahead adder (CLA) using two-phase all-N-transistor (ANT) blocks which are arranged in a PLA design style with power-aware pipelining is presented. The pull-up charging and pull-down discharging of the transistor arrays of the PLA are accelerated by two feedback MOS transistors between the evaluation NMOS blocks and the outputs. Both the added power-aware clock control circuit and clock generation circuit detecting data transition take advantage of shutting down the processing stages given identical inputs in two consecutive operations by keeping high clock level. The design keeps the advantage of high speed while having the effect of low power dissipation. The implantable neural stimulator assists patients to reconstruct transmission paths of neural signals by current stimulation. The proposed small DAC not only decreases the chip area and power dissipation by reducing transistor count, but also improves the linearity with higher current output performance. All of measured performances of the proposed DAC make the chip worthy of being implemented in a field application.

Abstract The tremendous progress in all aspects of signal processing technology has naturally been accompanied by a corresponding development of arithmetic techniques to provide high-speed operations at reasonable complexity. In the past, many architectural design efforts have focused on maximizing performance for frequently executed simple arithmetic operations such as addition and multiplication while left other rarely used operations ignored. In this dissertation, we firstly propose two design approaches for 64-b carry-lookahead adders (CLA) using a two-phase clocking dynamic CMOS logic since fast adders are the key elements in many digital circuits. Secondly, we place emphasis on the inner product operation since it is one of the most frequently used mathematical operations in the computation of digital neural networks. A ratioed 3-2 compressor is also presented to resolve several physical design problems that are not fully considered or implemented in previous research works. Finally we propose several fast 64b/32b integer dividers because the integer division is unavoidable in many important signal-processing applications.

Recent interest in approximate computation is driven by its potential to achieve large energy savings. We formally demonstrate an optimal way to reduce energy via voltage over-scaling at the cost of errors due to timing starvation in addition. A fundamental trade-off between error frequency and error magnitude in a timing-starved adder has been identified. We introduce a formal model to prove that for signal processing applications using a quadratic signal-to-noise ratio error measure, reducing bit-wise error frequency is sub-optimal. Instead, energy-optimal approximate addition requires limiting maximum error magnitude. Intriguingly, due to possible error patterns, this is achieved by reducing carry chains significantly below what is allowed by the timing budget for a large fraction of sum bits, using an aligned, fixed internal-carry structure for higher significance bits. We further demonstrate that remaining approximation error is reduced by realization of conditional bounding (CB) logic for lower significance bits. A key contribution is the formalization of an approximate CB logic synthesis problem that produces a rich space of Pareto-optimal adders with a range of quality-energy trade-offs. We show how CB logic can be customized to result in over- and under-estimating approximate adders, and how a dithering adder that mixes them produces zero-centered error distributions, and, in accumulation, a reduced-variance error. This work demonstrates synthesized approximate adders with energy up to 60% smaller than that of a conventional timing-starved adder, where a 30% reduction is due to the superior synthesis of inexact CB logic. When used in a larger system implementing an image-processing algorithm, energy savings of 40% are possible. / text

High performance, energy efficient logic style has always been a popular research topic in the field of very large scale integrated (VLSI) circuits because of the continuous demands of ever increasing circuit operating frequency. The invention of the dynamic logic in the 80s is one of the answers to this request as it allows designers to implement high performance circuit block, i.e., arithmetic logic unit (ALU), at an operating frequency that traditional static and pass transistor CMOS logic styles are difficult to achieve. However, the performance enhancement comes with several costs, including reduced noise margin,charge-sharing noise, and higher power dissipation due to higher data activity. Furthermore, dynamic logic has gradually lost its performance advantage over static logic due to the increased self-loading ratio in deep-submicron technology (65nm and below) because of the additional NMOS CLK footer transistor. Because of dynamic logic's limitations and diminished speed reward, a slowly rising need has emerged in the past decade to explore new logic style that goes beyond dynamic logic. In this thesis a constant delay (CD) logic style is proposed. The constant delay characteristic of this logic style regardless of the logic expression makes it suitable in implementing complicated logic expression such as addition. Moreover, CD logic exhibits a unique characteristic where the output is pre-evaluated before the inputs from the preceding stage is ready. This feature enables performance advantage over static and dynamic logic styles in a single cycle, multi-stage circuit block. Several design considerations including appropriate timing window width adjustment to reduce power consumption and maintain sufficient noise margin to ensure robust operations are discussed and analyzed. Using 65nm general purpose CMOS technology, the proposed logic demonstrates an average speed up of 94% and 56% over static and dynamic logic respectively in five different logic expressions. Post layout simulation results of 8-bit ripple carry adders conclude that CD-based design is 39% and 23% faster than the static and dynamic-based adders respectively. For ultra-high speed applications, CD-based design exhibits improved energy, power-delay product, and energy-delay product efficiency compared to static and dynamic counterparts.

In the era of Internet of Things and Big Data, unconventional techniques are rising to accommodate the large size of data and the resource constraints. New computing structures are advancing based on non-volatile memory technologies and different processing paradigms. Additionally, the intrinsic resiliency of current applications leads to the development of creative techniques in computations. In those applications, approximate computing provides a perfect fit to optimize the energy efficiency while compromising on the accuracy. In this work, we build probabilistic adders based on stochastic memristor. Probabilistic adders are analyzed with respect of the stochastic behavior of the underlying memristors. Multiple adder implementations are investigated and compared. The memristive probabilistic adder provides a different approach from the typical approximate CMOS adders. Furthermore, it allows for a high area saving and design exibility between the performance and power saving. To reach a similar performance level as approximate CMOS adders, the memristive adder achieves 60% of power saving. An image-compression application is investigated using the memristive probabilistic adders with the performance and the energy trade-off.

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With the emergence of quantum physics and computer science in the 20th century, a new era was born which can solve very difficult problems in a much faster rate or problems that classical computing just can't solve. In the 21st century, quantum computing needs to be used to solve tough problems in engineering, business, medical, and other fields that required results not today but yesterday. To make this dream come true, engineers in the semiconductor industry need to make the quantum circuits a reality. To realize quantum circuits and make them scalable, they need to be fault tolerant, therefore Clifford+T gates need to be implemented into those circuits. But the main issue is that in the Clifford+T gate set, T gates are expensive to implement. Carry Look-Ahead addition circuits have caught the interest of researchers because the number of gate layers encountered by a given qubit in the circuit (or the circuit's depth) is logarithmic in terms of the input size n. Therefore, this thesis focuses on optimizing previous designs of out-of-place and in-place Carry Look-Ahead Adders to decrease the T-count, sum of all T and T Hermitian transpose gates in a quantum circuit.

<p>Multiplications occur frequently in digital signal processing systems, communication systems, and other application specific integrated circuits. Multipliers, being relatively complex units, are deciding factors to the overall speed, area, and power consumption of digital computers. The diversity of application areas for multipliers and the ubiquity of multiplication in digital systems exhibit a variety of requirements for speed, area, power consumption, and other specifications. Traditionally, speed, area, and hardware resources have been the major design factors and concerns in digital design. However, the design paradigm shift over the past decade has entered dynamic power and static power into play as well.</p><p>In many situations, the overall performance of a system is decided by the speed of its multiplier. In this thesis, parallel multipliers are addressed because of their speed superiority. Parallel multipliers are combinational circuits and can be subject to any standard combinational logic optimization. However, the complex structure of the multipliers imposes a number of difficulties for the electronic design automation (EDA) tools, as they simply cannot consider the multipliers as a whole; i.e., EDA tools have to limit the optimizations to a small portion of the circuit and perform logic optimizations. On the other hand, multipliers are arithmetic circuits and considering arithmetic relations in the structure of multipliers can be extremely useful and can result in better optimization results. The different structures obtained using the different arithmetically equivalent solutions, have the same functionality but exhibit different temporal and physical behavior. The arithmetic equivalencies are used earlier mainly to optimize for area, speed and hardware resources.</p><p>In this thesis a design methodology is proposed for reducing dynamic and static power dissipation in parallel multiplier partial product reduction tree. Basically, using the information about the input pattern that is going to be applied to the multiplier (such as static probabilities and spatiotemporal correlations), the reduction tree is optimized. The optimization is obtained by selecting the power efficient configurations by searching among the permutations of partial products for each reduction stage. Probabilistic power estimation methods are introduced for leakage and dynamic power estimations. These estimations are used to lead the optimizers to minimum power consumption. Optimization methods, utilizing the arithmetic equivalencies in the partial product reduction trees, are proposed in order to reduce the dynamic power, static power, or total power which is a combination of dynamic and static power. The energy saving is achieved without any noticeable area or speed overhead compared to random reduction trees. The optimization algorithms are extended to include spatiotemporal correlations between primary inputs. As another extension to the optimization algorithms, the cost function is considered as a weighted sum of dynamic power and static power. This can be extended further to contain speed merits and interconnection power. Through a number of experiments the effectiveness of the optimization methods are shown. The average number of transitions obtained from simulation is reduced significantly (up to 35% in some cases) using the proposed optimizations.</p><p>The proposed methods are in general applicable on arbitrary multi-operand adder trees. As an example, the optimization is applied to the summation tree of a class of elementary function generators which is implemented using summation of weighted bit-products. Accurate transistor-level power estimations show up to 25% reduction in dynamic power compared to the original designs.</p><p>Power estimation is an important step of the optimization algorithm. A probabilistic gate-level power estimator is developed which uses a novel set of simple waveforms as its kernel. The transition density of each circuit node is estimated. This power estimator allows to utilize a global glitch filtering technique that can model the removal of glitches in more detail. It produces error free estimates for tree structured circuits. For circuits with reconvergent fanout, experimental results using the ISCAS85 benchmarks show that this method generally provides significantly better estimates of the transition density compared to previous techniques.</p>