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Sagot :
For a sequential circuit that detects the sequence 1011 using the Mealy model, we need to create state diagrams for both scenarios: when overlap is allowed and when overlap is not allowed.
Mealy Model with Overlap Allowed
In this case, the circuit can start detecting a new sequence before finishing the previous one if part of the new sequence is detected in the latter part of the previous one. Here’s the state diagram:
State S0: Initial state, waiting for 1.
Input 0: Remain in S0.
Input 1: Go to S1.
State S1: Detected 1, waiting for 0.
Input 0: Go to S2.
Input 1: Remain in S1.
State S2: Detected 10, waiting for 1.
Input 0: Return to S0.
Input 1: Go to S3.
State S3: Detected 101, waiting for 1.
Input 0: Return to S2.
Input 1: Go to S4 (output Z=1).
State S4: Detected 1011.
Input 0: Go to S2.
Input 1: Go to S1.
The output Z=1 occurs in the transition from S3 to S4.
Mealy Model with Overlap Not Allowed
In this case, once the sequence 1011 is detected, the circuit will reset and not allow overlapping detection of the sequence. Here’s the state diagram:
State S0: Initial state, waiting for 1.
Input 0: Remain in S0.
Input 1: Go to S1.
State S1: Detected 1, waiting for 0.
Input 0: Go to S2.
Input 1: Remain in S1.
State S2: Detected 10, waiting for 1.
Input 0: Return to S0.
Input 1: Go to S3.
State S3: Detected 101, waiting for 1.
Input 0: Return to S0.
Input 1: Go to S4 (output Z=1).
State S4: Detected 1011.
Input 0: Return to S0.
Input 1: Return to S0.
The output Z=1 occurs in the transition from S3 to S4.
Diagrams
Mealy Model with Overlap Allowed
1 0 1 0 1
(S0) ---> (S1) ---> (S2) ---> (S3) ---> (S4) --\ Z=1
^ \_____ / 1 | \_____ / 1 |
| 0 | 0
| |
\___________________________________/
Mealy Model with Overlap Not Allowed
1 0 1 0 1
(S0) ---> (S1) ---> (S2) ---> (S3) ---> (S4) --\ Z=1
^ \_____ / 1 | \_____ / 1 |
| 0 | 0
| |
\___________________________________/
The key difference is in the transitions out of state S4; for the non-overlap case, all transitions return to the initial state S0.
This setup ensures that the sequence detector behaves correctly based on the specifications given.
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