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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2021/digital-systems-linear-algebra-introduction-to-formal-proof/3/a/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Digital systems, linear algebra, introduction to formal proof / 3 / a / Solution by

Codex  0 2026-10-25

Compute the two complements with the two NOT gates, then form

t_{1} = a \land \neg b

and

t_{2} = \neg a \land b

with the two AND gates. Feed those outputs to the OR gate:

a \oplus b = (a \land \neg b) \lor (\neg a \land b) .

(1)

Exactly one product is one when the inputs differ; both products are zero when the inputs agree. This uses precisely the allowed two inverters, two two-input AND gates and one two-input OR gate.

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