A number generator sequences through numbers, 0, 1, 3, and 6. After 6, it goes back to O and continues the same counting sequence. A 3-bit binary number ABC is used to represent the numbers, whereby A is the MSB and C is the LSB. It is a self-correcting counter and all unused states will reset back to number 0. (a) Sketch the state transition diagram for the binary numbers. (3 marks) (b) Recall the operation of J-K flip-flops, derive the Booleans for each flip-flop inputs and show the state transition table. (12 marks) (c) Implement the number generator using J-K flip-flops and logic gates. (6 marks) (d) The propagation delay time for the NOT gate, AND gate, OR gate, and flip-flop are 5 ns, 10 ns, 20 ns, and 30 ns, respectively. Estimate the maximum clock frequency of the counter. (4 marks)