Exercise 7.29 (Complete Bi-Decomposition of the Incompletely Specified Function g2q(x), g2r(x)). Check, based on the allowed pairs of variables found for all types of bi-decompositions in Exercise 7.24, whether extended complete bi-decompositions exist for the incompletely specified function with the mark function g2q(x) and g2r(x). Calculate the decomposition functions of a complete bi-decomposition having the most variables in their decomposition sets. Practical tasks:

1 Load the TVL system e73dec3.sdt of Exercise 7.27. This TVL system includes the function g2q(x) as object number 30 and g2r(x) as object number 31.

2 Prepare a PRP that checks whether a one-to-two OR-bi-decomposition of the given ISF based on the known elementary OR-bi-decompositions exist.
3 Prepare a PRP that checks whether a one-to-two AND-bi-decomposition of the given ISF based on the known elementary AND-bi-decompositions exists.
4 Prepare a PRP that checks whether a one-to-two EXOR-bi-decomposition of the given ISF based on the known elementary EXOR-bi-decompositions exists.
5 Are there one-to-two OR-bi-decompositions?
6 Are there one-to-two AND-bi-decompositions?
7 Are there one-to-two EXOR-bi-decompositions?
8 Prepare a PRP that checks whether a two-to-two AND-bi-decomposition of the given ISF based on the known elementary AND-bi-decompositions exists.
9 Are there two-to-two AND-bi-decompositions?
10 Prepare a PRP that checks whether a one-to-three AND-bi-decomposition of the given ISF based on the known elementary AND-bi-decompositions exists.
11 Are there one-to-three AND-bi-decompositions?
12 Load the TVL system e73dec3.sdt of Exercise 7.27 in order to remove the intermediate results.
13 Calculate the mark function g3q(x) as object 32 and g3r(x) as object number 33 using the formulas (7.107) and (7.108) in [18] for the existing AND-bi-decomposition with regard to (x1, [x3, x4]). Select the function g3(x1, x2) to be realized in the multilevel circuit and store it as object 13. Show the Karnaugh-maps of the calculated mark functions and the selected function.
14 Calculate the mark functions h3q(x) as object 34 and h3r(x) as object number 35 using the formulas (7.109) and (7.110) in [18] for the existing AND-bi-decomposition with regard to (x1, [x3, x4]). Show the Karnaughmaps of the calculated mark functions.
15 Store TVL system as e73dec4.sdt for later use.