Design a sequential circuit with a $2-$bit input x y$,$ one output z and four states that

behaves as follows. Inputs xy represent the encoded value showing on a $4-$sided die $(1,2,3,4)$:

$$ xy$=00$ if roll is $1$

$$ xy$=01$ if roll is $2$

$$ xy$=10$ if roll is $3$

$$ xy$=11$ if roll is $4$

$-$ The output is $1$ when the present input roll brings the cumulative total to $4($add the value of the rolls$)$;

otherwise the output is $0.$

$-$ When the output is one $($because the cumulative total is $4),$ the total proceeds to reset to $0$ in the next state.

$-$ If any roll would make the running total exceed $4,$ that roll is skipped and the running total remains

unchanged. For example, the only way to change a present total of $3$ is to roll a $1.$