Design of a Sequence Detector (14.1)
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Design of a Sequence Detector (14.1)
Seq. ends in 101 --> Z=1 (no reset)Otherwise--> Z=0
Typical input/output sequence
Partial Soln. (Mealy Network):
Initially start in state S0 - the reset state
0 received - stay in S0
1 received go to a new state S1
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Design of a Sequence Detector (14.1)
Seq. ends in 101 --> Z=1 (no reset) otherwise--> Z=0
Partial Soln.:
0 received in S1 - go to a new state S2
1 received in S2 seq. (101) rec’d (Z=1)
-cannot go back to S0 (no reset)
-go back to state S1 since last 1 could
be part of a new seq.
Final State Graph:
1 received in S1 - stay in S1 (seq.
restarted)
0 received in S2 seq. (00) rec’d -must
reset to S0
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Design of a Sequence Detector (14.1)
Convert State Graph to State Table:Represent the threestates with two FF’s A and Bto obtain the transitiontable.
Seq. ends in 101 --> Z=1 (no reset) otherwise--> Z=0
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Design of a Sequence Detector (14.1)
Plot next state and Zmaps from transitiontable
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Design of a Sequence Detector (14.1)
From the next state and Z maps we obtained:
A+ = X’B, B+ = X, Z = XAIf D FF’s are used DA = A
+, DB = B+
which leads to the network:
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Design of a Sequence Detector (14.1 Moore)Seq. ends in 101 --> Z=1 (no reset) otherwise--> Z=0
For the Moore Network:When a 1 is rec’d to complete seq. (101)-must have Z=1 so must create a new
state S3 with output Z=1
Note the seq. 100 resets the network to
S0
Final State Graph
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Design of a Sequence Detector (14.1 Moore)
Convert State Graph to State Table:Represent the fourstates with two FF’s A and Bto obtain the transition table.FF input eqns. can be derived as was done for Mealy network.
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Seq. ends in 010 or 1001 --> Z=1Otherwise --> Z=0
Mealy Sequential Network (14.2)
Partial State Graph-gives Z=1 for seq. 010
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Seq. ends in 010 or 1001 --> Z=1Otherwise --> Z=0
Mealy Sequential Network (14.2)
Partial State Graph-additional states for seq. (1001)
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Seq. ends in 010 or 1001 --> Z=1Otherwise --> Z=0
Mealy Sequential Network (14.2)
Final State Graph-takes into account all otherinput sequences
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Z=1 if total no. of 1’s received is odd and at least two consecutive 0’s rec’d
Moore Sequential Network (14.2)
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Z=1 if total no. of 1’s received is odd and at least two consecutive 0’s rec’d
Moore Sequential Network (14.2)
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Guidelines for Construction of State Graphs
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14Final graph includes other seq.
11
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Soln.:
The repeating part of the sequence is generated usinga loop.
(A blank space above the slash indicates that the network has no otherInput than the clock.)
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States are based on the previous input pair. Don’t need separatestates for 00, 11 since neither input starts a seq. which leads to anoutput change.
However, for each previousInput, the output could be0 or 1, so we need six states.
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Example 3 cont’d
We can set up the state table shownbelow.
e.g. S4 row:
If 00 rec’d the input seq. has been10,00 so output does not change and
we go to S0.
If 01 rec’d the input seq. has been10,01 so output changes to 1 and
we go to S3.
If 11 rec’d the input seq. has been10,11 so output changes to 1 and
we go to S1.
If 10 rec’d the input seq. has been10,10 so output does not change and
we stay in S4.
01,11 --> 010,11 --> 110,01 --> change
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Example 3 cont’d
01,11 --> 010,11 --> 110,01 --> change
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• Coding schemes for serial data transmission– NRZ: nonreturn-to-zero– NRZI: nonreturn-to-zero-inverted
• 0 - same as the previous bit; 1 - complement of the previous bit
– RZ: return-to-zero• 0 – 0 for full bit time; 1 – 1 for the first half, 0 for the second half
– Manchester
A Converter for Serial Data Transmission: NRZ-to-Manchester
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Moore Network for NRZ-to-Manchester
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Moore Network for NRZ-to-Manchester
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Mealy Network for NRZ-to-Manchester