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Question 1 (30 pts.): Design a synchronous sequential circuit for detecting specific events. Circuit detects when there are at least two zeroes following after each other "..00.." or at least two ones "..11.." in the sequence of synchronous bits entering the input x. The circuit starts with x = 0 which means that one zero has entered the input. Detector output z should be '1' in the clock interval directly after the sequences has occurred. The sequence circuit is a Moore machine with positive edge triggered JK-flip-flops. Sample pattern: 01101010001010 x: 0101 Z:00 0 0 0 0 0 1 0 0 0 0 011000 a. (6 pts.) Draw the state diagram of the detector. b. (10 pts.) Use the binary code to encode the states and set up the encoded state table. c. (8 pts.) Obtain the minimized expressions for the inputs of the flip-flops and the output functions. d. (6 pts.) Sketch a schematic of your design.