1. Design a sequential logic circuit to check an input stream labeled X and to produce an output Z=1 for any input sequence ending in 101 and 1001. Use the following test sequence to verify your circuits operation:

X = 110100110010110 Z = 000100100010100 Make sure your circuit has a start state and the means to manually reset the flip-flops to the start state. Note that sequences may overlap, i.e., the circuit does not reset to the start state when an output Z=1 occurs. Testing your circuit will involve checking the correctness of every state and next states for all possible combinations of the input.

2. Design a sequential logic circuit to check an input stream labeled X and to produce an output Z=1 if the total number of zeros received is odd and the sequence 100 has occurred at least once. The total number of zeros received include before, during and after the sequence 100 is received. Use the following test sequence to verify your circuits operation:

X = 110100110010110 Z = 000001000100001 Make sure your circuit is a Moore circuit and it has a start state and the means to manually reset the flip- flops to the start state. Note that the circuit does not reset to the start state when an output Z=1 occurs. Testing your circuit will involve checking the correctness of every state and next states for all possible combinations of the input.