Design a pulse-mode asynchronous sequential machine for a tollgate (vending machine) problem as follows using SR flip-flops and draw the final circuit diagram:

A tollgate (vending machine) controller accepts only nickels (5c), dimes (10c), and quarts (25c), and generates control signal to actuate the lever to open the tollgate (or dispense a chosen item in case of vending machine) once 35c or more are received. The control signal is reset by a reset pulse generated upon passing of the car (or dispensing of the item). Even if the coins are dropped simultaneously, an electromechanical system separates them, and passes them across a sensor one by one. Depending upon the coin sensed, the sensor generates a pulse on a line earmarked for that coin. Taking those 3 lines as well as a fourth line for reset as the inputs to your system, you are required to design the digital system for generating the control signal. Please use the following state assignment:

S0 = 000, S5 = 001, S10 = 011, S15 = 010, S20 = 110, S25 = 111, S30 = 101, and S35M = 100. Here "SNUM" means a state in which the machine realized "NUM" (number) of cents. For example, S15 means that the machine realized so far 15c. S35M means the state in which 35 or more cents have been realized. The output z, the control signal, obviously is to be 1 in that state.

(1 Mark for State table + 6 marks for the derivation of final equations for the S0, R0, S1, R1, S2, and R2 functions required for the eight state machine using 24 Karnaugh maps + 2 marks for the circuit diagram = Total of 9 Marks.)