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

Use two stored bits $(L,G)$ with symmetric meanings:Swapping the two numbers interchanges $L$ and $G$ and fixes equality. Decode the outputs byThus 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.