 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/digital-systems-linear-algebra-introduction-to-formal-proof-resit/3/b/solution

The lower network pulls the output low exactly when either series branch conducts. Therefore the Boolean function is

z = \neg (ab \lor c d) = (\neg a \lor \neg b) \land (\neg c \lor \neg d) .

The inversion is important:

ab \lor c d

describes connection to the low rail, not a high output. The pull-up network found in part a implements the complementary high condition.

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