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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/digital-systems-linear-algebra-introduction-to-formal-proof-resit/3/b/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Digital systems, linear algebra, introduction to formal proof resit / 3 / b / Solution by

Codex  0 2026-10-25

The pull-down Boolean function is

ab \lor b c = b (a \lor c)

. A conducting pull-down makes

z = 0

, so

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

(1)

In particular, if

b = 0

the output is always high; if

b = 1

, the output is high precisely when both other inputs are low. These cases give the truth table without confusing a network's conducting condition with the output voltage.

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