Design an up-down counter that has an input 'X' and one output 'Y'. The specifications of the counter to be designed is as follows: • When X=1 it increments through the sequence 0,1,2,3,0,1,... 0, 1, 2, 3, 0, 1, ... with each clock tick. . • X=0 causes the counter to count in the reverse direction i.e. 0,3,2,1,0,3,2,1,0..... The system has one output 'Y', which is going to be equal to 1 (Y=1), only when the count of the counter is equal to 3 ONLY. The output Y=0, at all other conditions. Your circuit should use D Flip Flops. (i) Draw the state diagram of the counter (use a Moore machine). (4 marks) (ii) Give simplified expressions for the required next-state logic and output, and draw the sequential circuit (6 marks)

Fig: 1