Exercise 8.12 (Controlling Functions j1 and k1). The memory function sf1 of the non-deterministic finite-state machine defined in Exercise 8.11 shall be realized by a JK-flip-flop. Calculate the controlling functions j1 and k1 taking into consideration the freedom of the specified non-deterministic behavior. Restrict the behavior of the finite-state machine regarding the selected controlling functions j1 and k1. Practical tasks:

1 Load the final TVL system of Exercise 8.11. Object number 1 includes the non-deterministic system function F(x, s, sf , y) for which the circuit structure of the memory function sf1 must be calculated.

2 Map the behavior of the memory function sf1 to the behavior of controlling functions j1 and k1 using an appropriate list of phases of a JKflip-

flop taken from Table 8.3 in [18]. The system function F1(x, s, sf , y, j1, k1) will be created.

3 Restrict F1(x, s, sf , y, j1, k1) to the allowed behavior of the controlling functions j1 and k1 which results in F1jk(x, s, j1, k1).

4 Calculate the list of phases F1j(x, s, j1) for the controlling function j1 of the JK-flip-flop.

5 Calculate the don’t-care function j1ϕ(x, s).

6 Calculate the function j1q(x, s) that describes the ON-set of the incompletely specified function j1 and show the associated Karnaugh-map.

7 Calculate the function j1r(x, s) that describes the OFF-set of the incompletely specified function j1 and show the associated Karnaugh-map.

8 Select a simple function for the controlling functions j1 9 Restrict F1(x, s, sf , y, j1, k1) to the allowed behavior with regard the selected controlling functions j1.
10 Restrict the new system function F1(x, s, sf , y, j1, k1) into the allowed behavior F1jk(x, s, j1, k1) of the controlling functions j1 and k1.
11 Calculate the list of phases F1k(x, s, k1) for the controlling function k1 of the JK-flip-flop.
12 Calculate the don’t-care function k1ϕ(x, s).
13 Calculate the function k1q(x, s) that describes the ON-set of the incompletely specified function k1 and show the associated Karnaugh-map.
14 Calculate the function k1r(x, s) that describes the OFF-set of the incompletely specified function k1 and show the associated Karnaugh-map.
15 Select a simple function for the controlling function k1.
16 Restrict F1(x, s, sf , y, j1, k1) to the allowed behavior with regard the selected controlling function k1.
17 Remove all information about j1 and k1 from the final system function F1(x, s, sf , y, j1, k1) and store the restricted result F(x, s, sf , y) as object number 6.
18 Which effect has the selection of the controlling functions j1 and k1 to the remaining system function F(x, s, sf , y)?
19 Store the TVL system as e8302.sdt for later use.