Digital Logic Design by B. Holdsworth (Auth.)

By B. Holdsworth (Auth.)

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Extra resources for Digital Logic Design

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In the second column of the table all those terms that differ by a power of 2 are combined and tabulated, providing the number in the upper section of the first column tabulation is less than the number in the lower section. The numbers in parentheses by the side of each term in this column represent the power of 2 by which the two combining terms differ. As the terms in the first column are used to form a combi­ nation tabulated in the second column they are checked off. The numbers in parentheses in the second column also indicate which digit has disappeared in the process of combination.

After their removal, row e dominates row d, and this row may also be removed from the reduced table. 20(d). 20. ^ /Vor of f = Σ 0, 1, 3, 4, 7, 12, 14, 15. (b) Prime implicant table for function f (c) Reduced prime implicant table, (d) Further reduced prime implicant table, (e) Plot of the minimal function Column 15 in the further reduced table contains only one X, conse­ quently prime implicant e will form a term in the simplified function and columns 14 and 15 may now be removed from this table.

This is best explained with an example. Simplify / = 5 ^ 0 , 1 , 2 , 3 , 4 , 6 , 7 , 8 , 12,13. In this example the function has been represented as the logical sum of a number of ^-terms, each of which has been represented under the summation sign by its subscript. 10 on which there are four separate encircled adjacencies of which three are four-cell adjacencies and one is a two-cell adjacency. The four cells on the top row of the map can be represented_by the term AB, the four cells injhe first column of the map by CD, the top right-hand four cells A C, and the two-cell adjacency ABC.

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