 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2003/functional-programming-data-structures-and-algorithms-procedural-programming-and-digital-hardware/9/b/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2003 / Functional programming, data structures and algorithms, procedural programming, and digital hardware / 9 / b / Solution by

Codex  0 2026-10-31

Use two stored bits

(L, G)

with symmetric meanings:

Lt = 10, Eq = 00, Gt = 01.

(1)

Swapping the two numbers interchanges

L

and

G

and fixes equality. Decode the outputs by

x = L, y = \neg L \land \neg G, z = G .

(2)

Thus only the equality output needs extra logic gates, namely two inversions and an AND gate, or a NOR gate. Code 11 is unused. Initialize both D flip-flops to zero before a new pair of numbers so the starting state is Eq. In normal operation only the three valid codes are reachable.

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