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Extra info for An Introduction to Digital Logic
Hill and G. R. Peterson. Introduction to Switching Theory and Logical Design, Wiley (1968). 4 E. Mendelson. Boolean Algebra and Switching Circuits, McGraw-Hill (1970). 1 A simple design example As an introduction to simple logic design procedures, we shall consider a system which is required to act as a safety interlock to prevent an electric motor running in a situation when damage can result. Such safety interlock systems have been used for many years of course and often use relay circuits. Although the systems may be and often are designed by purely intuitive means, boolean techniques may be applied and will be used in this case.
The rule for implementing the simplification procedure is similar to that used when looping two cells only. If four cells are looped, four terms in the original boolean expression can be combined into a single term eliminating two variables. The variables which are eliminated are those which are not equal in the four cells. An easy way of identifying which variables are eliminated is to note that if a loop crosses the boundary of a defined area of the map then the variable associated with that area is eliminated from the term.
6 The final stage is to design a system which will generate F from inputs A, X, Y and Z. This system is shown in figure 3. 7. INTRODUCTION TO DIGITAL LOGIC 30 A----------------------~ F z----------------------------------------~ F= [A. "Y)]. 4 An equivalence system As a further demonstration of the design procedure for combinational logic systems, consider the design for a circuit with four inputs A, 8, X and Y and two outputs F and G. F is required to be 1 when A =X and 8 = Y. G is required to be 1 when A -=/=X and 8-=/= Y.