Q$\mathrm{.}2$ You need to design a special modulo counter that normally counts in modulo$-8$ sequence of $0,1,2,3,4,5,6,7,0,1,2,3,4,5,6,7,0,1,2,3,...$ as its external output. The initial state of the counter is the state with an output of $0$ and modulo$\_$half as $0.$

Whenever the modulo$\_$half input changes to $1,$ the count sequence needs to appropriately become modulo$-4$ sequence of $0,1,2,3,0,1,2,3,0,1,...$ subsequently from the counting stage that it was received. When the modulo$\_$half input becomes $0,$ the counter moves back to its normal modulo$-8$ counting sequence from the next counting stage onwards.

For illustration purpose, if the counter reaches the counting stage of $6$ in its sequence of normal counting and modulo$\_$half becomes $1,$ then the counter$$s next output value will be $3($and not $7)$ and it will follow the modulo$-4$ counting sequence till modulo$\_$half stays as $1.$ Similarly, if the counter reaches the stage of output as $3$ in its normal counting and modulo$\_$half becomes $1,$ then the counter$$s next output value will be $0($and not $4)$ and it will follow the modulo$-4$ counting sequence. When counter output reaches $3$ with modulo$\_$half as $1$ and then if modulo$\_$half becomes $0,$ the counter$$s next output value will be $4($and not $0)$ and it will subsequently follow the normal modulo$-8$ counting sequence.

Give the state diagram for such a special modulo counter.