By Doris M. Cochran and Coleman J. Goin
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A storage operation can hold input data and output it at a later time. Logic functions are similar to propositional statements and can be completely and uniquely specified by a truth table that gives the output values for each and every possible combination of inputs. A binary connective is a function that relates the output of a binary system to its inputs. By considering all possible functions of two inputs the fundamentallogic operations can be identified. Finally, the relevance of Boolean algebra to logic design was assessed.
ABC . ABC. 2. The 2nd canonical form can be obtained directly from the truth table without having to resort to lengthy algebra. 2 we can identify each maxterm with an entry that gives a zero output, provided we represent each inverted variable in the maxterm with aland each normal variable with a O. Note the 'CR followed by AND' structure. , BCC==~~ Inputs OR level AND level Output Fig. 2 A 2nd canonical form circuit. 33 For example: Input ABC = 000 gives F=O and forms the maxterm (A+B+C). Input ABC = 001 gives F=O and forms the maxterm (A+B+C) and so on.
BCC==~~ Inputs OR level AND level Output Fig. 2 A 2nd canonical form circuit. 33 For example: Input ABC = 000 gives F=O and forms the maxterm (A+B+C). Input ABC = 001 gives F=O and forms the maxterm (A+B+C) and so on. Compare this rule with the 1st canonical rule. It is the opposite in every respect. The rule for obtaining the 2nd canonical form is therefore: for each entry in the truth table with an output at 0, create an OR of the inputs using the normal variable, if its value is 0, or its inverted value, if the input is at '1.