Exercise 7.40 (Test Pattern Calculated for a Sensible Point of a Local Branch). Calculate all test patterns for the sensible point nx4 in the circuit of Fig. 7.16 on page 190 designed in Section 3. using the bi-decomposition.

Use (7.152) . . . (7.156) of [18] and the equation system of Exercise 7.35, Task 3 as basis. Practical tasks:

1 Define a Boolean space of 32 variables and assign the variables appearing in the circuit of Fig. 7.16.

2 Modify the equation system of Exercise 7.35, Task 3 such that the NOTgate nx4 is described explicitly, and the controlled inputs of nx4 are labeled by the model variables s1 and s2, respectively. Solve this system of logic equations.

3 Prepare for the sensible point nx4 both the branch function FB(t, s1, s2)

and the function FT (nx4, t) that describe the controllability condition.

4 Prepare VTs of the internal variables of the circuit, first of all model variables of the local branch s1, s2, t, secondly of each of these variables separately, and finally of s1, s2.

5 Calculate the possible behavior for the local branch of nx4 based on

(7.152) of [18].

6 Calculate the required behavior for the local branch of nx4 based on

(7.154) of [18].

7 Calculate all existing test patterns for the signal source of the local branch of nx4 based on (7.156) of [18].

8 Calculate all existing test patterns for the signal target s1 on the OR-gate of the local branch of nx4 based on (7.156) of [18].

9 Calculate all existing test patterns for the signal target s2 on the EXORgate of the local branch of nx4 based on (7.156) of [18].

10 Calculate all these test patterns which can detect errors on the signal source of the branch nx4, but not on the signal targets s1 and s2, respectively.

11 Calculate all these test patterns which can detect errors on the target s1 of the branch nx4, but not on the associated signal source.

12 Calculate all these test patterns which can detect errors on the target s2 of the branch nx4, but not on the associated signal source.

13 Verify whether there are test patterns which detect errors on both signal targets of the branch nx4 but not on the signal source