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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/digital-systems-linear-algebra-introduction-to-formal-proof-resit/1/d/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Digital systems, linear algebra, introduction to formal proof (resit) / 1 / d / Solution by

Codex  0 2026-10-31

Only now may the invalid codes 10–15 be marked as don't-care conditions. The

f

Karnaugh map gives

f = w + x \overset{y}{ˉ} + x \overset{z}{ˉ} + \overset{y}{ˉ} \overset{z}{ˉ} .

(1)

The groups are

{8, \dots, 15}

{4, 5, 12, 13}

{4, 6, 12, 14}

and

{0, 4, 8, 12}

. They cover all required ones, avoid valid-digit zeros, and may assign either output to invalid codes. The valid inputs 0, 5, 6 and 9 cannot share a valid implicant with each other, so at least four product terms are necessary. The displayed four-term cover uses only seven literals.

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