Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Digital systems, linear algebra, introduction to formal proof / 1 / e

The inclusive range contains $2147483648=2^{31}$ distinct states. An $n$-bit binary counter has $2^n$ states, so 31 JK flip-flops in total are necessary and sufficient for the required capacity: add 28 to the three shown.

This is a capacity calculation. The printed positive-edge, uncomplemented-output cascade visits these codes in descending order. To obtain increasing numerical order one must change the cascade clock polarity, for example clocking each positive-edge stage from the preceding complemented output.