By Edward L. Braun
Electronic desktop layout, good judgment, Circuitry, and Synthesis
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Extra info for Digital Computer Design. Logic, Circuitry, and Synthesis
Y = ABC + ABC + ABC + . . (3-14) Such an expression may be obtained directly from a truth table by noting all combinations of input variables for which the output variable has a value of 1. Equation (3-15) is obtained from Eq. (3-14) by the principle of dualization. It states that any Boolean equation can be written as a logical product of logical sums* (generally abbreviated, for convenience, to "a product of sums") each of which contains all input variables. A representation of this type is said to be in conjunctive normal form.
One of the most important of these is that a Boolean algebraic equation can be manipulated to yield equivalent functional forms. Then one can choose to mechanize that particular form which best satisfies certain specified physical requirements. The discussion following is in tended to describe a number of techniques that are commonly used to sim plify a Boolean equation or convert it to an equivalent form more desirable in the light of certain physical requirements. 1. , its removal does not alter values of the expression, that term is said to be redundant.
First of all, it is useful to employ symbolic addresses in the initial preparation of relatively long programs because alterations may be made in one part of the program without the need for extensive changes of addresses through out. For example, if actual addresses were used and a required instruction inadvertently omitted, then all addresses beyond that point, as well as all references to such addresses, would have to be altered. Of course, after the program has been adequately checked, and is ready to be inserted into the computer, actual addresses would be substituted for the symbolic addresses.
Digital Computer Design. Logic, Circuitry, and Synthesis by Edward L. Braun