Exercise 7.22 (All Minimal Disjunctive Forms). Create the sets of all minimal disjunctive forms based on the set of all prime conjunctions given in Fig. 7.7

a) for the function given in Fig. 7.4 b). Evaluate these sets with regard to the number of required prime conjunctions. Enumerate the shortest minimal disjunctive forms. Practical tasks:

1 Create a Boolean space for the cover function covf (p).

2 Create a TVL in K-form having the columns of the variables p1 . . . p14.

Add rows to this TVL such that the 1 marks usable prime conjunctions for a function cube and fill the remaining positions with dashes −. In order to do this compare systematically the ternary vectors of the function given in Fig. 7.4

b) on page 172 with the prime conjunctions given in Fig. 7.7

a) on page 177 for allowed covers. Equal rows can be removed immediately.

3 Transform the TVL created in K-form into a minimized TVL in D-form as described above. Remove all such rows that can be absorbed by any other row.

4 Each row of the minimized cover function in D-form represents a minimal disjunctive form of the basic function. Evaluate the found sets with regard to the number of required prime conjunctions.
5 Create and show TVLs of the shortest minimal disjunctive forms.