1. Design a sequential circuit with two flip-flops A and B and two inputs E and X. If E=0, the circuit remains in the same state, regardless of the value of X. When E=1 and X=1, the circuit goes through the state transitions from 00 to 01 to 10 to 11, back to 00, and then repeats. When E=1 and X=0, the circuit goes through the state transitions from 00 to 11 to 10 to 01, back to 00, and then repeats. Design the circuit using Positive-edge-triggered D-FF.
2. A single-input, single-output sequential circuit is to be designed that recognizes only the two input sequences 0110 and 1111 applied to its inputs any time they occur in the input stream. If any of these two sequences is detected the output will be 1, otherwise it will be 0.
   1. Show the state diagram for this circuit assuming no detection of overlapping sequences.
   2. Show the state diagram for this circuit assuming detection of overlapping sequences