 Solution

Use four-variable Karnaugh maps with rows $AB=00,01,11,10$ and columns $Cx=00,01,11,10$, both in Gray code order. A dash denotes an unused present state. The maps for the three next-state bits areFor $A^{+}$, join its sole one with the dash directly below it. For $B^{+}$, use the four-cell groups $Ax$ and $B\bar{C}$, and the two-cell group $\bar{B}Cx$; the last group wraps between the top and bottom rows. For $C^{+}$, join the one at row $01$, column $00$ to the dash below it; the one at row $00$, column $01$ is isolated. These prime implicants giveHere products mean Boolean conjunction and sums mean Boolean disjunction. The $D$ inputs are the desired next-state bits of the three D flip-flops. The equations are independent of the unused values except for the explicitly chosen Karnaugh map groups.