devices the techniques were tailored to gate networks of the type described above. The term gate was alread in use in the forties to denote the logical elements discussed earlier. There are very many good references on Boolean algebra and we may quote only a selected few of them. Suffice it to mention the texts by Hill and Peterson [1974], Kohavi [ 1978], and Hohn [1966]. These books give sufficiently rigorous formulation of the subject, tailored to the analysis and the design of combinational the Boolean techniques used in connection with relay circuits. (Some of the s also contain a discussion of omit this topic, which has been but totally overshadowed by the impressive development of electronic networks. The reader interested in studying the relation of switching algebra to Boolean algebras in general is referred to Preparata and Yeh 1973] for an eler Defining Terms Boolean algebra: The algebra of logical values enabling the logical designer to obtain expressions for digital Boolean expressions: Expressions of logical variables constructed using the connectives and, or, and not Boolean functions: Common designations of binary functions of binary variables. Combinational logic: Interconnections of memory-free digital elements. Switching theory: The theory of digital circuits viewed as interconnections of elements whose output can switch between the logical values of 0 and 1 Related Topic 79.2 Logic Gates(IC) References G Boole, An Investigation of the Laws of Thought, New York: Dover Publication, 1954 E J. Hill and G.R. Peterson, Introduction to Switching Theory and Logical Design, New York: Wiley, 1974. F.E. Hohn, Applied Boolean Algebra, New York: Macmillan, 1966 Z. Kohavi, Switching and Finite Automata Theory, New York: McGraw-Hill, 1978. E.P. Preparata and R.T. Yeh, Introduction to Discrete Structures, Reading, Mass. Addison C.E. Shannon,A symbolic analysis of relay and switching circuits, Trans. AIEE, vol. 57, 3-723,1938. 81.2 Logic circuits Richard S. Sandie Section 81.2 deals with two-state(high or low, I or 0, or true or false) logic circuits. Two-state logic circuits can be broken down into two major types of circuits: combinational logic circuits and sequential logic circuits. By definition, the external output signals of combinational logic circuits are totally dependent on the external input signals applied to the circuit. In contrast, the output signals of sequential logic circuits are dependent on all or part of the present state output signals of the circuit that are fed back as input signals to the circuit as well as any external input signals if they should exist. Sequential logic circuits can be subdivided into synchro nous or clock-mode circuits and asynchronous circuits. Asynchronous circuits can be further divided into fundamental-mode circuits and pulse-mode circuits. Fig 81.15 is the graphic classification of logic circuits Combinational logic circuits The block diagram in Fig. 81.16 illustrates the model for combinational logic circuits. The logic elements inside ock entitled combinational logic circuit can be any configuration of two-state logic elements such that the signals are totally dependent on the input signals to the circuit as indicated by the functional relationships in the figure e 2000 by CRC Press LLC© 2000 by CRC Press LLC devices the techniques were tailored to gate networks of the type described above. The term gate was already in use in the forties to denote the logical elements discussed earlier. There are very many good references on Boolean algebra and we may quote only a selected few of them. Suffice it to mention the texts by Hill and Peterson [1974], Kohavi [1978], and Hohn [1966]. These books give a sufficiently rigorous formulation of the subject, tailored to the analysis and the design of combinational networks. In addition, like most of the earlier books, Hohn’s and Kohavi’s texts also contain a discussion of the Boolean techniques used in connection with relay circuits. (Some of the more recent works completely omit this topic, which has been but totally overshadowed by the impressive development of electronic networks.) The reader interested in studying the relation of switching algebra to Boolean algebras in general is referred to Preparata and Yeh [1973] for an elementary introduction. Defining Terms Boolean algebra: The algebra of logical values enabling the logical designer to obtain expressions for digital circuits. Boolean expressions: Expressions of logical variables constructed using the connectives and, or, and not. Boolean functions: Common designations of binary functions of binary variables. Combinational logic: Interconnections of memory-free digital elements. Switching theory: The theory of digital circuits viewed as interconnections of elements whose output can switch between the logical values of 0 and 1. Related Topic 79.2 Logic Gates (IC) References G. Boole, An Investigation of the Laws of Thought, New York: Dover Publication, 1954. F.J. Hill and G.R. Peterson, Introduction to Switching Theory and Logical Design, New York: Wiley, 1974. F.E. Hohn, Applied Boolean Algebra, New York: Macmillan, 1966. Z. Kohavi, Switching and Finite Automata Theory, New York: McGraw-Hill, 1978. F.P. Preparata and R.T. Yeh, Introduction to Discrete Structures, Reading, Mass.: Addison-Wesley, 1973. C.E. Shannon, “A symbolic analysis of relay and switching circuits,” Trans. AIEE, vol. 57, pp. 713–723, 1938. 81.2 Logic Circuits Richard S. Sandige Section 81.2 deals with two-state (high or low, 1 or 0, or true or false) logic circuits. Two-state logic circuits can be broken down into two major types of circuits: combinational logic circuits and sequential logic circuits. By definition, the external output signals of combinational logic circuits are totally dependent on the external input signals applied to the circuit. In contrast, the output signals of sequential logic circuits are dependent on all or part of the present state output signals of the circuit that are fed back as input signals to the circuit as well as any external input signals if they should exist. Sequential logic circuits can be subdivided into synchro￾nous or clock-mode circuits and asynchronous circuits. Asynchronous circuits can be further divided into fundamental-mode circuits and pulse-mode circuits. Fig. 81.15 is the graphic classification of logic circuits. Combinational Logic Circuits The block diagram in Fig. 81.16 illustrates the model for combinational logic circuits. The logic elements inside the block entitled combinational logic circuit can be any configuration of two-state logic elements such that the output signals are totally dependent on the input signals to the circuit as indicated by the functional relationships in the figure