Sunday, 8 April 2018

Six Variable K Map Examples

A six-variable K-map is shown in Fig. 2.30, which also shows cell designations. This consists of  a group of 4 four-variable K-maps. It can be seen that the reduction process becomes highly complicated with six variables because locating  similar positions in the individual maps is a very difficult task. Entries are made as per the designations of the cells shown in Fig. 2.30.  It may be noted that the individual charts are designated as 00, 01, 11, and 10, respectively. The cell designations begin from 000000 (corresponding to decimal 0) to 111111 (corresponding to decimal 63) as shown. As in the case of the five-variable K-map, entries in similar cells can be combined to eliminate the involve variable (or variables) and thus simplify the given logic function. Example 8 will illustrate this.


Example 8: Simplify S(12, 13, 14, 15, 28, 29, 30, 31, 44, 45, 46, 47, 48, 49, 50, 51, 60, 61, 62, 63).

Solution: Figure 2.31 shows the entries for Example 8.
The encircled five quads can be combined to form into two main groups. Group 1 consists of  four quads whose individual members are (12, 13, 14, 15), (28, 29, 39, 31), (44, 45, 46, 47), and (60, 61, 62, 63), respectively. Group 2 consists of just one quad whose members are (48, 49, 50, 51). The final solution is:
                                                            S = cd + abc′d′                 (2.32)



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