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# Lecture Notes

This chapter 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.

This chapter 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.

This chapter 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.

This chapter 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 behavioural models to show the alternative ways available for describing combinational circuits in Verilog HDL.

This chapter 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.