1

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

2

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

3

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

14Final graph includes other seq.

11

15

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