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.

Synthesis of Finite State Machines: Functional Optimization is one of two monographs devoted to the synthesis of Finite State Machines (FSMs). This volume addresses functional optimization, whereas the second addresses logic optimization. By functional optimization here we mean the body of techniques that: compute all permissible sequential functions for a given topology of interconnected FSMs, and select a `best' sequential function out of the permissible ones. The result is a symbolic description of the FSM representing the chosen sequential function. By logic optimization here we mean the steps that convert a symbolic description of an FSM into a hardware implementation, with the goal to optimize objectives like area, testability, performance and so on. Synthesis of Finite State Machines: Functional Optimization is divided into three parts. The first part presents some preliminary definitions, theories and techniques related to the exploration of behaviors of FSMs. The second part presents an implicit algorithm for exact state minimization of incompletely specified finite state machines (ISFSMs), and an exhaustive presentation of explicit and implicit algorithms for the binate covering problem. The third part addresses the computation of permissible behaviors at a node of a network of FSMs and the related minimization problems of non-deterministic finite state machines (NDFSMs). Key themes running through the book are the exploration of behaviors contained in a non-deterministic FSM (NDFSM), and the representation of combinatorial problems arising in FSM synthesis by means of Binary Decision Diagrams (BDDs). Synthesis of Finite State Machines: Functional Optimization will be of interest to researchers and designers in logic synthesis, CAD and design automation.

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. Table of Contents: Calculating Maximum Clock Frequency / Improving Design Performance / Finite State Machine with Datapath (FSMD) Design / Embedded Memory Usage in Finite State Machine with Datapath (FSMD) Designs

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.

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 . . .

A unique guide to using both modeling and simulation in digital systems design Digital systems design requires rigorous modeling and simulation analysis that eliminates design risks and potential harm to users. Introduction to Digital Systems: Modeling, Synthesis, and Simulation Using VHDL introduces the application of modeling and synthesis in the effective design of digital systems and explains applicable analytical and computational methods. Through step-by-step explanations and numerous examples, the author equips readers with the tools needed to model, synthesize, and simulate digital principles using Very High Speed Integrated Circuit Hardware Description Language (VHDL) programming. Extensively classroom-tested to ensure a fluid presentation, this book provides a comprehensive overview of the topic by integrating theoretical principles, discrete mathematical models, computer simulations, and basic methods of analysis. Topical coverage includes: Digital systems modeling and simulation Integrated logic Boolean algebra and logic Logic function optimization Number systems Combinational logic VHDL design concepts Sequential and synchronous sequential logic Each chapter begins with learning objectives that outline key concepts that follow, and all discussions conclude with problem sets that allow readers to test their comprehension of the presented material. Throughout the book, VHDL sample codes are used to illustrate circuit design, providing guidance not only on how to learn and master VHDL programming, but also how to model and simulate digital circuits. Introduction to Digital Systems is an excellent book for courses in modeling and simulation, operations research, engineering, and computer science at the upper-undergraduate and graduate levels. The book also serves as a valuable resource for researchers and practitioners in the fields of operations research, mathematical modeling, simulation, electrical engineering, and computer science.

A comprehensive guide to the theory and design of hardware-implemented finite state machines, with design examples developed in both VHDL and SystemVerilog languages. Modern, complex digital systems invariably include hardware-implemented finite state machines. The correct design of such parts is crucial for attaining proper system performance. This book offers detailed, comprehensive coverage of the theory and design for any category of hardware-implemented finite state machines. It describes crucial design problems that lead to incorrect or far from optimal implementation and provides examples of finite state machines developed in both VHDL and SystemVerilog (the successor of Verilog) hardware description languages. Important features include: extensive review of design practices for sequential digital circuits; a new division of all state machines into three hardware-based categories, encompassing all possible situations, with numerous practical examples provided in all three categories; the presentation of complete designs, with detailed VHDL and SystemVerilog codes, comments, and simulation results, all tested in FPGA devices; and exercise examples, all of which can be synthesized, simulated, and physically implemented in FPGA boards. Additional material is available on the book's Website. Designing a state machine in hardware is more complex than designing it in software. Although interest in hardware for finite state machines has grown dramatically in recent years, there is no comprehensive treatment of the subject. This book offers the most detailed coverage of finite state machines available. It will be essential for industrial designers of digital systems and for students of electrical engineering and computer science.