Logic Synthesis for FPGA-Based Finite State Machines

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Publisher : Springer
ISBN 13 : 3319242024
Total Pages : 287 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Logic Synthesis for FPGA-Based Finite State Machines by : Alexander Barkalov

Download or read book Logic Synthesis for FPGA-Based Finite State Machines written by Alexander Barkalov and published by Springer. This book was released on 2015-10-15 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses control units represented by the model of a finite state machine (FSM). It contains various original methods and takes into account the peculiarities of field-programmable gate arrays (FPGA) chips and a FSM model. It shows that one of the peculiarities of FPGA chips is the existence of embedded memory blocks (EMB). The book is devoted to the solution of problems of logic synthesis and reduction of hardware amount in control units. The book will be interesting and useful for researchers and PhD students in the area of Electrical Engineering and Computer Science, as well as for designers of modern digital systems.

Logic Synthesis for Finite State Machines Based on Linear Chains of States

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Publisher : Springer
ISBN 13 : 3319598376
Total Pages : 228 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Logic Synthesis for Finite State Machines Based on Linear Chains of States by : Alexander Barkalov

Download or read book Logic Synthesis for Finite State Machines Based on Linear Chains of States written by Alexander Barkalov and published by Springer. This book was released on 2017-06-24 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses Moore finite state machines (FSMs) implemented with field programmable gate arrays (FPGAs) including look-up table (LUT) elements and embedded memory blocks (EMBs). To minimize the number of LUTs in FSM logic circuits, the authors propose replacing a state register with a state counter. They also put forward an approach allowing linear chains of states to be created, which simplifies the system of input memory functions and, therefore, decreases the number of LUTs in the resulting FSM circuit. The authors combine this approach with using EMBs to implement the system of output functions (microoperations). This allows a significant decrease in the number of LUTs, as well as eliminating a lot of interconnections in the FSM logic circuit. As a rule, it also reduces the area occupied by the circuit and diminishes the resulting power dissipation. This book is an interesting and valuable resource for students and postgraduates in the area of computer science, as well as for designers of digital systems that included complex control units

Logic Synthesis for Fpga-Based Mealy Finite State Machines

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Author :
Publisher : CRC Press
ISBN 13 : 9781032882277
Total Pages : 0 pages
Book Rating : 4.8/5 (822 download)

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Book Synopsis Logic Synthesis for Fpga-Based Mealy Finite State Machines by : Alexander Barkalov

Download or read book Logic Synthesis for Fpga-Based Mealy Finite State Machines written by Alexander Barkalov and published by CRC Press. This book was released on 2024-12-04 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to logic synthesis of field programmable gate array (FPGA)-based circuits of Mealy finite state machines (FSM). Three new methods of state assignment are proposed which allows obtaining FSM circuits required minimum amount of internal chip resources. Logic Synthesis for FPGA-Based Mealy Finite State Machines: Structural Decomposition in Logic Design contains several original synthesis and optimization methods based on structural decomposition of FPGA-based FSM circuits developed by the authors. To optimize FSM circuits, the authors introduce the use three of methods of state assignment: twofold, extended, and composite. These methods allow for creating two-or three level architectures of FSM circuits. The authors also demonstrate how the proposed methods, FSM architectures and synthesis methods can replace known solutions based on either functional decomposition or classical methods of structural decomposition. The authors also show how these architectures have regular systems of interconnections and demonstrate positive features as compared to methods based on functional decomposition including producing circuits with fewer elements, that are faster and consume less power than their counterparts. The book includes experimental results proving efficiency of the proposed solutions and compares the numbers in Look-up Tables (LUTs), showing performance (maximum operating frequency) and power consumption for various methods of state assignment. The audience for this book is students researchers, and engineers specializing in computer science/ engineering, electronics, and telecommunications. It will be especially useful for engineers working with in the scope of algorithms, hardware-based software accelerators and control units, and systems based on the use of FPGA's.

Finite State Machine Logic Synthesis for Complex Programmable Logic Devices

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Publisher : Springer Science & Business Media
ISBN 13 : 3642361668
Total Pages : 182 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Finite State Machine Logic Synthesis for Complex Programmable Logic Devices by : Robert Czerwinski

Download or read book Finite State Machine Logic Synthesis for Complex Programmable Logic Devices written by Robert Czerwinski and published by Springer Science & Business Media. This book was released on 2013-01-12 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a monograph devoted to logic synthesis and optimization for CPLDs. CPLDs' macrocell can also be interpreted as programmable AND-fixed OR structure, well known as PAL-based structure. The question is: what should be done when the number of implicants representing function exceeds the number of product terms available in a logic block. The answer is ... in the book. Logic synthesis and optimization methods dedicated for PAL-based structures are proposed. The methods strive to find the optimum fit for the combinational logic and finite state machines to the structure of the logic device and aim at area and speed optimization. The theoretical background and complete strategies are richly illustrated with examples and figures.

Synthesis and Optimization of FPGA-Based Systems

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Publisher : Springer Science & Business Media
ISBN 13 : 3319047086
Total Pages : 443 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Synthesis and Optimization of FPGA-Based Systems by : Valery Sklyarov

Download or read book Synthesis and Optimization of FPGA-Based Systems written by Valery Sklyarov and published by Springer Science & Business Media. This book was released on 2014-03-14 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is composed of two parts. The first part introduces the concepts of the design of digital systems using contemporary field-programmable gate arrays (FPGAs). Various design techniques are discussed and illustrated by examples. The operation and effectiveness of these techniques is demonstrated through experiments that use relatively cheap prototyping boards that are widely available. The book begins with easily understandable introductory sections, continues with commonly used digital circuits, and then gradually extends to more advanced topics. The advanced topics include novel techniques where parallelism is applied extensively. These techniques involve not only core reconfigurable logical elements, but also use embedded blocks such as memories and digital signal processing slices and interactions with general-purpose and application-specific computing systems. Fully synthesizable specifications are provided in a hardware-description language (VHDL) and are ready to be tested and incorporated in engineering designs. A number of practical applications are discussed from areas such as data processing and vector-based computations (e.g. Hamming weight counters/comparators). The second part of the book covers the more theoretical aspects of finite state machine synthesis with the main objective of reducing basic FPGA resources, minimizing delays and achieving greater optimization of circuits and systems.

Logic Synthesis for FPGA-Based Control Units

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Author :
Publisher : Springer Nature
ISBN 13 : 3030382958
Total Pages : 247 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Logic Synthesis for FPGA-Based Control Units by : Alexander Barkalov

Download or read book Logic Synthesis for FPGA-Based Control Units written by Alexander Barkalov and published by Springer Nature. This book was released on 2020-01-08 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on control units, which are a vital part of modern digital systems, and responsible for the efficiency of controlled systems. The model of a finite state machine (FSM) is often used to represent the behavior of a control unit. As a rule, control units have irregular structures that make it impossible to design their logic circuits using the standard library cells. Design methods depend strongly on such factors as the FSM used, specific features of the logic elements implemented in the FSM logic circuit, and the characteristics of the control algorithm to be interpreted. This book discusses Moore and Mealy FSMs implemented with FPGA chips, including look-up table elements (LUT) and embedded memory blocks (EMB). It is crucial to minimize the number of LUTs and EMBs in an FSM logic circuit, as well as to make the interconnections between the logic elements more regular, and various methods of structural decompositions can be used to solve this problem. These methods are reduced to the presentation of an FSM circuit as a composition of different logic blocks, the majority of which implement systems of intermediate logic functions different (and much simpler) than input memory functions and FSM output functions. The structural decomposition results in multilevel FSM circuits having fewer logic elements than equivalent single-level circuits. The book describes well-known methods of structural decomposition and proposes new ones, examining their impact on the final amount of hardware in an FSM circuit. It is of interest to students and postgraduates in the area of Computer Science, as well as experts involved in designing digital systems with complex control units. The proposed models and design methods open new possibilities for creating logic circuits of control units with an optimal amount of hardware and regular interconnections.

Logic Synthesis for FSM-Based Control Units

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Publisher : Springer Science & Business Media
ISBN 13 : 3642043097
Total Pages : 245 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Logic Synthesis for FSM-Based Control Units by : Alexander Barkalov

Download or read book Logic Synthesis for FSM-Based Control Units written by Alexander Barkalov and published by Springer Science & Business Media. This book was released on 2009-11-25 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the hardware implementation of control algorithms represented by graph-schemes of algorithm. It includes new methods of logic synthesis and optimization for logic circuits of Mealy and Moore FSMs oriented on both ASIC and FPLD.

Logic Synthesis for VLSI-Based Combined Finite State Machines

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Author :
Publisher : Springer Nature
ISBN 13 : 3031160274
Total Pages : 305 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Logic Synthesis for VLSI-Based Combined Finite State Machines by : Alexander Barkalov

Download or read book Logic Synthesis for VLSI-Based Combined Finite State Machines written by Alexander Barkalov and published by Springer Nature. This book was released on 2022-11-24 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to design and optimization of control units represented by combined finite state machines (CFSMs). The CFSMs combine features of both Mealy and Moore FSMs. Having states of Moore FSM, they produce output signals of both Mealy and Moore types. To optimize the circuits of CFSMs, we propose to use optimization methods targeting both Mealy and Moore FSMs. The book contains some original synthesis and optimization methods targeting hardware reduction in VLSI-based CFSM circuits. These methods take into account the peculiarities of both a CFSM model and a VLSI chip in use. The optimization is achieved due to combining classical optimization methods with new methods proposed in this book. These new methods are a mixed encoding of collections of microoperations and a twofold state assignment in CFSMs. All proposed methods target reducing the numbers of arguments in systems of Boolean functions representing CFSM circuits. Also, we propose to use classes of pseudoequivalent states of Moore FSMs to reduce the number of product terms in these systems.The book includes a lot of examples which contributes to a better understanding of the features of the synthesis methods under consideration. This is the first book entirely devoted to the problems associated with synthesis and optimization of VLSI-based CFSMs. We hope that the book will be interesting and useful for students and PhD students in the area of Computer Science, as well as for designers of various digital systems. We think that proposed CFSM models enlarge the class of models applied for implementation of control units with modern VLSI chips.

Finite State Machine Datapath Design, Optimization, and Implementation

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Author :
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1598295292
Total Pages : 124 pages
Book Rating : 4.5/5 (982 download)

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Book Synopsis Finite State Machine Datapath Design, Optimization, and Implementation by : Justin Davis

Download or read book Finite State Machine Datapath Design, Optimization, and Implementation written by Justin Davis and published by Morgan & Claypool Publishers. This book was released on 2008 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite State Machine Datapath Design, Optimization, and Implementation explores the design space of combined FSM/Datapath implementations. The lecture starts by examining performance issues in digital systems such as clock skew and its effect on setup and hold time constraints, and the use of pipelining for increasing system clock frequency. This is followed by definitions for latency and throughput, with associated resource tradeoffs explored in detail through the use of dataflow graphs and scheduling tables applied to examples taken from digital signal processing applications. Also, design issues relating to functionality, interfacing, and performance for different types of memories commonly found in ASICs and FPGAs such as FIFOs, single-ports, and dual-ports are examined. Selected design examples are presented in implementation-neutral Verilog code and block diagrams, with associated design files available as downloads for both Altera Quartus and Xilinx Virtex FPGA platforms. A working knowledge of Verilog, logic synthesis, and basic digital design techniques is required. This lecture is suitable as a companion to the synthesis lecture titled Introduction to Logic Synthesis using Verilog HDL.

Foundations of Embedded Systems

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Publisher : Springer
ISBN 13 : 3030119610
Total Pages : 167 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Foundations of Embedded Systems by : Alexander Barkalov

Download or read book Foundations of Embedded Systems written by Alexander Barkalov and published by Springer. This book was released on 2019-02-04 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to embedded systems (ESs), which can now be found in practically all fields of human activity. Embedded systems are essentially a special class of computing systems designed for monitoring and controlling objects of the physical world. The book begins by discussing the distinctive features of ESs, above all their cybernetic-physical character, and how they can be designed to deliver the required performance with a minimum amount of hardware. In turn, it presents a range of design methodologies. Considerable attention is paid to the hardware implementation of computational algorithms. It is shown that different parts of complex ESs could be implemented using models of finite state machines (FSMs). Also, field-programmable gate arrays (FPGAs) are very often used to implement different hardware accelerators in ESs. The book pays considerable attention to design methods for FPGA-based FSMs, before the closing section turns to programmable logic controllers widely used in industry. This book will be interesting and useful for students and postgraduates in the area of Computer Science, as well as for designers of embedded systems. In addition, it offers a good point of departure for creating embedded systems for various spheres of human activity.

Logic Synthesis for Compositional Microprogram Control Units

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Publisher : Springer Science & Business Media
ISBN 13 : 3540692851
Total Pages : 283 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Logic Synthesis for Compositional Microprogram Control Units by : Alexander Barkalov

Download or read book Logic Synthesis for Compositional Microprogram Control Units written by Alexander Barkalov and published by Springer Science & Business Media. This book was released on 2008-07-17 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the very important parts of any digital system is the control unit, coordin- ing interplay of other system blocks. As a rule, control units have irregular str- ture, which makes process of their logic circuits design very sophisticated. In case of complex logic controllers, the problem of system design is reduced practically to the design of control units. Actually, we observe a real technical boom connected with achievements in semiconductor technology. One of these is the development of integrated circuit known as the "systems-on-a-programmable- chip" (SoPC), where the number of elements approaches one billion. Because of the extreme complexity of microchips, it is very important to develop effective design methods oriented on particular properties of logical elements. Solution of this problem permits impr- ing functional capabilities of the target digital system inside single SoPC chip. As majority of researches point out, design methods used in case of industrial packages are, in case of complex digital system design, far from optimal. Similar problems concern the design of control units with standard ?eld-programmable logic devices (FPLD), such as PLA, PAL, GAL, CPLD, and FPGA. Let us point out that modern SoPC are based on CPLD or FPGA technology. Thus, the development of eff- tive design methods oriented on FPLD implementation of logic circuits used in the control units still remains the problem of great importance.

Computer Information Systems and Industrial Management

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Publisher : Springer
ISBN 13 : 3319591053
Total Pages : 722 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Computer Information Systems and Industrial Management by : Khalid Saeed

Download or read book Computer Information Systems and Industrial Management written by Khalid Saeed and published by Springer. This book was released on 2017-05-16 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 16th IFIP TC8 International Conference on Computer Information Systems and Industrial Management, CISIM 2017, held in Bialystok, Poland, in June 2017. The 60 regular papers presented together with 5 keynotes were carefully reviewed and Selected from 85 submissions. They are organized in the following topical sections: algorithms; biometrics and pattern recognition applications; data analysis and information retrieval; engineering of enterprise software products; industrial management and other applications; modelling and optimization; various aspects of computer security.

Logic Synthesis Using Synopsys®

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Publisher : Springer Science & Business Media
ISBN 13 : 1475723709
Total Pages : 317 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Logic Synthesis Using Synopsys® by : Pran Kurup

Download or read book Logic Synthesis Using Synopsys® written by Pran Kurup and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic synthesis has become a fundamental component of the ASIC design flow, and Logic Synthesis Using Synopsys® has been written for all those who dislike reading manuals but who still like to learn logic synthesis as practised in the real world. The primary focus of the book is Synopsys Design Compiler®: the leading synthesis tool in the EDA marketplace. The book is specially organized to assist designers accustomed to schematic capture based design to develop the required expertise to effectively use the Compiler. Over 100 `classic scenarios' faced by designers using the Design Compiler have been captured and discussed, and solutions provided. The scenarios are based both on personal experiences and actual user queries. A general understanding of the problem-solving techniques provided will help the reader debug similar and more complicated problems. Furthermore, several examples and dc-shell scripts are provided. Specifically, Logic Synthesis Using Synopsys® will help the reader develop a better understanding of the synthesis design flow, optimization strategies using the Design Compiler, test insertion using the Test Compiler®, commonly used interface formats such as EDIF and SDF, and design re-use in a synthesis-based design methodology. Examples have been provided in both VHDL and Verilog. Audience: Written with CAD engineers in mind to enable them to formulate an effective synthesis-based ASIC design methodology. Will also assist design teams to better incorporate and effectively integrate synthesis with their existing in-house design methodology and CAD tools.

Technology Mapping for LUT-Based FPGA

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Publisher : Springer Nature
ISBN 13 : 3030604888
Total Pages : 207 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Technology Mapping for LUT-Based FPGA by : Marcin Kubica

Download or read book Technology Mapping for LUT-Based FPGA written by Marcin Kubica and published by Springer Nature. This book was released on 2020-11-07 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers selected topics of automated logic synthesis dedicated to FPGAs. The authors focused on two main problems: decomposition of the multioutput functions and technology mapping. Additionally, the idea of using binary decision diagrams (BDD) in these processes was presented. The book is a scientific monograph summarizing the authors’ many years of research. As a result, it contains a large number of experimental results, which makes it a valuable source for other researchers. The book has a significant didactic value. Its arrangement allows for a gradual transition from basic things (e.g., description of logic functions) to much more complex issues. This approach allows less advanced readers to better understand the described problems. In addition, the authors made sure that the issues described in the book were supported by practical examples, thanks to which the reader can independently analyze even the most complex problems described in the book.

Sequential Logic Synthesis

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Publisher : Springer Science & Business Media
ISBN 13 : 1461536286
Total Pages : 238 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Sequential Logic Synthesis by : Pranav Ashar

Download or read book Sequential Logic Synthesis written by Pranav Ashar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 3. 2 Input Encoding Targeting Two-Level Logic . . . . . . . . 27 3. 2. 1 One-Hot Coding and Multiple-Valued Minimization 28 3. 2. 2 Input Constraints and Face Embedding 30 3. 3 Satisfying Encoding Constraints . . . . . . . 32 3. 3. 1 Definitions . . . . . . . . . . . . . . . 32 3. 3. 2 Column-Based Constraint Satisfaction 33 3. 3. 3 Row-Based Constraint Satisfaction . . 37 3. 3. 4 Constraint Satisfaction Using Dichotomies . 38 3. 3. 5 Simulated Annealing for Constraint Satisfaction 41 3. 4 Input Encoding Targeting Multilevel Logic. . 43 3. 4. 1 Kernels and Kernel Intersections . . . 44 3. 4. 2 Kernels and Multiple-Valued Variables 46 3. 4. 3 Multiple-Valued Factorization. . . . . 48 3. 4. 4 Size Estimation in Algebraic Decomposition . 53 3. 4. 5 The Encoding Step . 54 3. 5 Conclusion . . . . . . . . . 55 4 Encoding of Symbolic Outputs 57 4. 1 Heuristic Output Encoding Targeting Two-Level Logic. 59 4. 1. 1 Dominance Relations. . . . . . . . . . . . . . . . 59 4. 1. 2 Output Encoding by the Derivation of Dominance Relations . . . . . . . . . . . . . . . . . . . . . 60 . . 4. 1. 3 Heuristics to Minimize the Number of Encoding Bits . . . . . . . . . . . . 64 4. 1. 4 Disjunctive Relationships . . . . . . . . . . . 65 4. 1. 5 Summary . . . . . . . . . . . . . . . . . . 66 . . 4. 2 Exact Output Encoding Targeting Two-Level Logic. 66 4. 2. 1 Generation of Generalized Prime Implicants . 68 4. 2. 2 Selecting a Minimum Encodeable Cover . . . 68 4. 2. 3 Dominance and Disjunctive Relationships to S- isfy Constraints . . . . . . . . . . . 70 4. 2. 4 Constructing the Optimized Cover 73 4. 2. 5 Correctness of the Procedure . . 73 4. 2. 6 Multiple Symbolic Outputs . . .

Design of Digital Systems and Devices

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 3642175457
Total Pages : 372 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Design of Digital Systems and Devices by : Marian Adamski

Download or read book Design of Digital Systems and Devices written by Marian Adamski and published by Springer Science & Business Media. This book was released on 2011-02-04 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic design of digital devices is a very important part of the Computer Science. It deals with design and testing of logic circuits for both data-path and control unit of a digital system. Design methods depend strongly on logic elements using for implementation of logic circuits. Different programmable logic devices are wide used for implementation of logic circuits. Nowadays, we witness the rapid growth of new and new chips, but there is a strong lack of new design methods. This book includes a variety of design and test methods targeted on different digital devices. It covers methods of digital system design, the development of theoretical base for construction and designing of the PLD–based devices, application of UML for digital design. A considerable part of the book is devoted to design methods oriented on implementing control units using FPGA and CPLD chips. Such important issues as design of reliable FSMs, automatic design of concurrent logic controllers, the models and methods for creating infrastructure IP services for the SoCs are also presented. The editors of the book hope that it will be interesting and useful for experts in Computer Science and Electronics, as well as for students, who are viewed as designers of future digital devices and systems.

Synthesis of Finite State Machines

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Publisher : Springer Science & Business Media
ISBN 13 : 1461561558
Total Pages : 382 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Synthesis of Finite State Machines by : Tiziano Villa

Download or read book Synthesis of Finite State Machines written by Tiziano Villa and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Synthesis of Finite State Machines: Logic Optimization is the second in a set of two monographs devoted to the synthesis of Finite State Machines (FSMs). The first volume, Synthesis of Finite State Machines: Functional Optimization, addresses functional optimization, whereas this one addresses logic optimization. The result of functional optimization is a symbolic description of an FSM which represents a sequential function chosen from a collection of permissible candidates. Logic optimization is the body of techniques for converting a symbolic description of an FSM into a hardware implementation. The mapping of a given symbolic representation into a two-valued logic implementation is called state encoding (or state assignment) and it impacts heavily area, speed, testability and power consumption of the realized circuit. The first part of the book introduces the relevant background, presents results previously scattered in the literature on the computational complexity of encoding problems, and surveys in depth old and new approaches to encoding in logic synthesis. The second part of the book presents two main results about symbolic minimization; a new procedure to find minimal two-level symbolic covers, under face, dominance and disjunctive constraints, and a unified frame to check encodability of encoding constraints and find codes of minimum length that satisfy them. The third part of the book introduces generalized prime implicants (GPIs), which are the counterpart, in symbolic minimization of two-level logic, to prime implicants in two-valued two-level minimization. GPIs enable the design of an exact procedure for two-level symbolic minimization, based on a covering step which is complicated by the need to guarantee encodability of the final cover. A new efficient algorithm to verify encodability of a selected cover is presented. If a cover is not encodable, it is shown how to augment it minimally until an encodable superset of GPIs is determined. To handle encodability the authors have extended the frame to satisfy encoding constraints presented in the second part. The covering problems generated in the minimization of GPIs tend to be very large. Recently large covering problems have been attacked successfully by representing the covering table with binary decision diagrams (BDD). In the fourth part of the book the authors introduce such techniques and extend them to the case of the implicit minimization of GPIs, where the encodability and augmentation steps are also performed implicitly. Synthesis of Finite State Machines: Logic Optimization will be of interest to researchers and professional engineers who work in the area of computer-aided design of integrated circuits.