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.

This book is devoted to the 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 the structural decomposition of FPGA-based FSM circuits developed by the authors. To optimize FSM circuits, the authors introduce the use of three methods of state assignment: twofold, extended, and composite. These methods allow for the creation of 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 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 the efficiency of the proposed solutions and compares the numbers in Look-up Tables (LUTs), showing the 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 within the scope of algorithms, hardware-based software accelerators and control units, and systems based on the use of FPGAs.

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

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.

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.

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.

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.