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 / b / Solution

Five distinct states require three D flip-flops, since $2^2<5\le 2^3$. Choose the state encoding $S_i$ equal to the three-bit binary expansion of $i$. Write the present bits as $A,B,C$, in decreasing significance. The state transition table isThe dashes are don't-care conditions for minimizing the logic. They do not prescribe what the actual circuit will do in those unused states; part (e) determines that from the chosen equations.