Re$-$implement the vending machine controller from lecture, but extend it to give change by releasing

nickels when appropriate.

The inputs are:

$,$: single bit inputs indicating whether a nickel or a dime $($but never both$)$ have been inserted

$,$: the usual clock and active low reset inputs

The outputs are:

$$: a single bit, set to $1$ for one clock cycle to vend an item

$$: a single bit, set to $1$ for one cycle to return a nickel $($a nickel can only be returned when an

item is vended$)$

As before, the machine accept only nickels and dimes, and vends a single item whose price is $15.$ This

new machine should accept and credit all coins entered, including while vending or returning change.

Note: the item and change should be produced as soon as possible, and this depends on the type of finite state machine used.

$($a$)$ Draw a state transition diagram for a Moore implementation of this machine. Your design should minimize the number of states.

b$)$ Using the minimum necessary number of D flip$-$flops, set the state encoding, and derive SoPexpressions for the next state and output logic