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Question Question How do you detect a sequence of "1101" arriving serially from a signal line?
Answer Answer Sequence detector : A sequence detector gives an output of 1 on detecting the given sequence else the output is zero.

Ex : if the given sequence to be detected is 111
and input stream is 1 1 0 1 1 1 0 0 1 0 1 1 1 1 1
the output should be 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1.

Soln:
One of the different possible ways to detect a sequence is using a Mealy type FSM.

Using the following table the State machine can be designed.
since the number of bits in the sequence 1101 is 4 we have 4 states

------------------------------------------------------
|PS | Seq detected by the state | NS/output |
| | |---------------|
| | | X=0 | X=1 |
|-----------------------------------------------------
| S1 | - | S1/0 | S2/0 |
|----------------------------------------------------|
| S2 | 1 | S1/0 | S3/0 |
|----------------------------------------------------|
| S3 | 11 | S4/0 | S3/0 |
|----------------------------------------------------|
| S4 | 110 | S1/0 | S2/1 |
|----------------------------------------------------|



when in state S4 (PS),and input(X) from the sequence is 1,the sequence "1101" has been detected once and (to find the next state select the longest "seq identified by a state" column that matches part of the sequence 1101--ie.,1 or 01 or 101 ....)the NS is S2 since the sequence detected by the state S2 is 1(in 1101- 01 or 101 ,etc are not present in the seq identified by the state column ,).

Consider the case when input is 1101101 the output is 0001001.ie., the sequence detector is able to identify overlapping sequences.

Submitted by Methuku Surekha (methuku_surekha@yahoo.com)


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