Exercise $1(7$ points$)$ A sequential circuit has two inputs $x1$ and $x0,$ and an output $z.$ Consider the natural

number composed by the last two bits of $x1,$ followed by the last two bits of $0.$ If the division between

that number and $3$ has a reminder of $1,$ the output is equal to $1.$ Otherwise the output is equal to $0.$

Design the state transition diagram and the sequential circuit.

Overlaps are allowed. Ignore the first output $($it can be set to any value$).$

Example: INPUT: $x111001$

$x000100$

Output: $z,-0001$