 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2018/digital-systems-linear-algebra-introduction-to-formal-proof/1/c/solution

With the encoding in part (b), $y = A$ is a valid Moore machine output equation. Among reachable states,

A = 1

exactly at

S_{4}

. This uses unused output-table entries as don't-care conditions. If one instead wants the output to be zero in every unused state, use

y = A \overset{ˉ}{B} \overset{ˉ}{C}

; that extra requirement does not change any output from a valid state.

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