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2. (a) Draw the state diagram for a FSM with states mod 7, and the transitions are c -+ 2c mod 7 or mod 7 based on some binary input I, the outputs (Zl, 742) are (c mod 3, c + 1 mod 2) and (c + 1 mod 3, c mod 2) respectively. (b) Encode the states of the FSM by bits. List your encoding in a table or show the encoding on your diagram. (c) Write the truth table for the next state function and the outputs. (d) Implement circuit for next state using a decoder. (e) Implement circuit for the output Zl using 8-1 multiplexers. (f) Implement circuit in terms of AND, OR, NOT gates for Z2 using the simplest SOP formula for Z2 (g) Use the above circuits to implement the FSM