Exercise 7.32 (Complete Bi-Decomposition of h2(x)). Execute the bidecomposition of the completely specified h2(x) = h2q(x) which depends on the variables (x2, x3, x4) and verify the result. Practical tasks:

1 Load the TVL system e73dec6.sdt of Exercise 7.31. This TVL system includes the function h2q(x) as object number 38, h2r(x) = h2q(x)

as object number 39, g3(x) as object number 13, and g1(x) as object number 10.

2 Prepare a PRP that checks for each pair of the three variables based on

(7.86) in [18] whether an OR-bi-decomposition exists.

3 Prepare a PRP that checks for each pair of the three variables based on

(7.90) in [18] whether an AND-bi-decomposition exists.

4 Prepare a PRP that checks for each pair of the three variables based on

(7.93) in [18] whether an EXOR-bi-decomposition exists.

5 Are there strong one-to-one OR-bi-decompositions?

6 Are there strong one-to-one AND-bi-decompositions?

7 Are there strong one-to-one EXOR-bi-decompositions?

8 Are there strong one-to-two bi-decompositions?

9 Calculate the function g5 of the existing disjoint AND-bi-decomposition with regard to (x2, [x3, x4]) based on (7.91) in [18] as object 18.

10 Calculate the function h5 of the existing disjoint AND-bi-decomposition with regard to (x2, [x3, x4]) based on (7.92) in [18] as object 19.

11 Calculate the function h2(x2, x3, x4) to be realized in the multilevel circuit and store it as object 17. Show the Karnaugh-map of the selected function h2(x2, x3, x4).

12 Remove the intermediate TVL and store for later use the TVL system as e73dec7.sdt.