# TAILIEUCHUNG - Complete Digital Design P2

## Digital Fundamentals is irrelevant: AC . It may appear tempting to create a product term consisting of the three boxes on the bottom edge of the K-map. This is not valid because it does not result in all boxes sharing a common product relationship, and therefore violates the power-of-two rule mentioned previously. Upon completing the K-map, all product terms are summed to yield a ﬁnal and simpliﬁed Boolean equation that relates the input variables and the output: Y = B + AC . Functions of four variables are just as easy to solve using a K-map. Beyond four variables, it is. | 10 Digital Fundamentals is irrelevant AC . It may appear tempting to create a product term consisting of the three boxes on the bottom edge of the K-map. This is not valid because it does not result in all boxes sharing a common product relationship and therefore violates the power-of-two rule mentioned previously. Upon completing the K-map all product terms are summed to yield a final and simplified Boolean equation that relates the input variables and the output Y B AC . Functions of four variables are just as easy to solve using a K-map. Beyond four variables it is preferable to break complex functions into smaller subfunctions and then combine the Boolean equations once they have been determined. Figure shows an example of a completed Karnaugh map for a hypothetical function of four variables. Note the overlap between several groups to achieve a simplified set of product terms. The lager a group is the fewer unique terms will be required to represent its logic. There is nothing to lose and something to gain by forming a larger group whenever possible. This K-map has four product terms that are summed for a final result Y AC BC ABD ABCD . In both preceding examples each result box in the truth table and Karnaugh map had a clearly defined state. Some logical relationships however do not require that every possible result necessarily be a one or a zero. For example out of 16 possible results from the combination of four variables only 14 results may be mandated by the application. This may sound odd but one explanation could be that the particular application simply cannot provide the full 16 combinations of inputs. The specific reasons for this are as numerous as the many different applications that exist. In such circumstances these so-called don t care results can be used to reduce the complexity of your logic. Because the application does not care what result is generated for these few combinations you can arbitrarily set the results to 0s or 1s so that .

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