By A. Potton (auth.)
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Extra info for An Introduction to Digital Logic
Quine. The Problem of Simplifying Truth Functions. Am. math. , 59 (Oct. 1952), 521-31. ). McCluskey. 'Minimisation of Boolean Functions'. Bell Syst. tech. , 35 (Nov. 1956) 1417-44. 5 Bistable Systems Logic systems discussed up to this point have had the property that the logical state of the output at a particular point in time was completely determined by the logic levels at the inputs at that time. We now turn our attention to systems in which the logical state of the output at a particular time may be determined by the logic levels which existed at the input at some previous time.
Shannon. 'Symbolic Analysis of Relay and Switching Circuits', Trans. Am. lnst. elect. Engrs, 57, (1938) 713-23. 3 F. J. 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.
3. 20 shows the various cell loopings. 9 'Don't care' situations We now suppose that in the previous problem, the specification for the system is again changed this time such that the value ofF for the condition N 1 = N 2 is irrelevant, that is it may be 0 or 1. 4. 21, the 'don't care' cells containing a dagger may be assumed to contain 0 or 1 to suit ones own convenience. This leads to some simplification of the logical expression describing the circuit operation. 10 Minimisation with functions of more than four variables The Karnaugh map technique can be extended to handle functions of five, six or more variables by using maps consisting of arrays of cells in three or more dimensions.