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/c/solution

Joining the two middle nodes makes the upper lower-network transistors, controlled by , parallel with each other. The lower transistors, controlled by , are also parallel. These two parallel groups are in series, so the lower conducting condition becomes .
Its dual upper network must be two parallel branches, one containing the series PMOS transistor pair , the other the series pair . This is the right panel of the original drawing. Its condition is . Merely leaving the old upper network unchanged would break CMOS complementarity for some inputs, allowing a supply short rather than defining the required logic.

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