## Chapter Summary

The following is a brief summary of the topics that are covered in each chapter.

**Chapter 1** presents the various binary systems suitable for representing information in digital systems. The binary number system is explained and binary codes are illustrated. Examples are given for addition and subtraction of signed binary numbers and decimal numbers in binary‐coded decimal (BCD) format.

**Chapter 2** introduces the basic postulates of Boolean algebra and shows the correlation between Boolean expressions and their corresponding logic diagrams. All possible logic operations for two variables are investigated, and the most useful logic gates used in the design of digital systems are identified. This chapter also introduces basic CMOS logic gates.

**Chapter 3** covers the map method for simplifying Boolean expressions. The map method is also used to simplify digital circuits constructed with AND‐OR, NAND, or NOR gates. All other possible two‐level gate circuits are considered, and their method of implementation is explained. Verilog HDL is introduced together with simple examples of gate‐level models.

**Chapter 4** outlines the formal procedures for the analysis and design of combinational circuits. Some basic components used in the design of digital systems, such as adders and code converters, are introduced as design examples. Frequently used digital logic functions such as parallel adders and subtractors, decoders, encoders, and multiplexers are explained, and their use in the design of combinational circuits is illustrated. HDL examples are given in gate‐level, dataflow, and behavioral models to show the alternative ways available for describing combinational circuits in Verilog HDL. The procedure for writing a simple test bench to provide stimulus to an HDL design is presented.

**Chapter 5** outlines the formal procedures for analyzing and designing clocked (synchronous) sequential circuits. The gate structure of several types of flip‐flops is presented together with a discussion on the difference between level and edge triggering. Specific examples are used to show the derivation of the state table and state diagram when analyzing a sequential circuit. A number of design examples are presented with emphasis on sequential circuits that use D‐type flip‐flops. Behavioral modeling in Verilog HDL for sequential circuits is explained. HDL Examples are given to illustrate Mealy and Moore models of sequential circuits.

**Chapter 6** deals with various sequential circuit components such as registers, shift registers, and counters. These digital components are the basic building blocks from which more complex digital systems are constructed. HDL descriptions of shift registers and counter are presented.

**Chapter 7** deals with random access memory (RAM) and programmable logic devices. Memory decoding and error correction schemes are discussed. Combinational and sequential programmable devices such as ROMs, PLAs, PALs, CPLDs, and FPGAs are presented.

**Chapter 8** deals with the register transfer level (RTL) representation of digital systems. The algorithmic state machine (ASM) chart is introduced. A number of examples demonstrate the use of the ASM chart, ASMD chart, RTL representation, and HDL description in the design of digital systems. The design of a finite state machine to control a datapath is presented in detail, including the realistic situation in which status signals from the datapath are used by the state machine that controls it. This chapter is the most important chapter in the book as it provides the student with a systematic approach to more advanced design projects.

**Chapter 9** outlines experiments that can be performed in the laboratory with hardware that is readily available commercially. The operation of the ICs used in the experiments is explained by referring to diagrams of similar components introduced in previous chapters. Each experiment is presented informally and the student is expected to design the circuit and formulate a procedure for checking its operation in the laboratory. The lab experiments can be used in a stand‐alone manner too and can be accomplished by a traditional approach, with a breadboard and TTL circuits, or with an HDL/synthesis approach using FPGAs. Today, software for synthesizing an HDL model and implementing a circuit with an FPGA is available at no cost from vendors of FPGAs, allowing students to conduct a significant amount of work in their personal environment before using prototyping boards and other resources in a lab. Circuit boards for rapid prototyping circuits with FPGAs are available at a nominal cost, and typically include push buttons, switches, seven‐segment displays, LCDs, keypads, and other I/O devices. With these resources, students can work prescribed lab exercises or their own projects and get results immediately.

**Chapter 10** presents the standard graphic symbols for logic functions recommended by an ANSI/IEEE standard. These graphic symbols have been developed for small‐scale integration (SSI) and medium‐scale integration (MSI) components so that the user can recognize each function from the unique graphic symbol assigned. The chapter shows the standard graphic symbols of the ICs used in the laboratory experiments.

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