1 Design of a Sequence Detector (14.1) Seq. ends in > Z=1 (no reset) Otherwise--> Z=0 Typical input/output sequence Partial Soln. (Mealy Network): Initially start in state S 0 - the reset state 0 received - stay in S 0 1 received go to a new state S 1

2 Design of a Sequence Detector (14.1) Seq. ends in > Z=1 (no reset) otherwise--> Z=0 Partial Soln.: 0 received in S 1 - go to a new state S 2 1 received in S 2 seq. (101) rec’d (Z=1) -cannot go back to S 0 (no reset) -go back to state S 1 since last 1 could be part of a new seq. Final State Graph: 1 received in S 1 - stay in S 1 (seq. restarted) 0 received in S 2 seq. (00) rec’d -must reset to S 0

3 Design of a Sequence Detector (14.1) Convert State Graph to State Table: Represent the three states with two FF’s A and B to obtain the transition table. Seq. ends in > Z=1 (no reset) otherwise--> Z=0

4 Design of a Sequence Detector (14.1) Plot next state and Z maps from transition table

5 Design of a Sequence Detector (14.1) From the next state and Z maps we obtained: A + = X’B, B + = X, Z = XA If D FF’s are used D A = A +, D B = B + which leads to the network:

6 Design of a Sequence Detector (14.1 Moore) Seq. ends in > 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 S 3 with output Z=1 Note the seq. 100 resets the network to S 0 Final State Graph

7 Design of a Sequence Detector (14.1 Moore) Convert State Graph to State Table: Represent the four states with two FF’s A and B to obtain the transition table. FF input eqns. can be derived as was done for Mealy network.

8 Seq. ends in 010 or > Z=1 Otherwise --> Z=0 Mealy Sequential Network (14.2) Partial State Graph -gives Z=1 for seq. 010

9 Seq. ends in 010 or > Z=1 Otherwise --> Z=0 Mealy Sequential Network (14.2) Partial State Graph -additional states for seq. (1001)

10 Seq. ends in 010 or > Z=1 Otherwise --> Z=0 Mealy Sequential Network (14.2) Final State Graph -takes into account all other input sequences

11 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)

12 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)

13 Guidelines for Construction of State Graphs

14 Final graph includes other seq. 1111

15 Soln.: The repeating part of the sequence is generated using a loop. (A blank space above the slash indicates that the network has no other Input than the clock.)

16 States are based on the previous input pair. Don’t need separate states for 00, 11 since neither input starts a seq. which leads to an output change. However, for each previous Input, the output could be 0 or 1, so we need six states.

17 Example 3 cont’d We can set up the state table shown below. e.g. S 4 row: If 00 rec’d the input seq. has been 10,00 so output does not change and we go to S 0. If 01 rec’d the input seq. has been 10,01 so output changes to 1 and we go to S 3. If 11 rec’d the input seq. has been 10,11 so output changes to 1 and we go to S 1. If 10 rec’d the input seq. has been 10,10 so output does not change and we stay in S 4. 01,11 --> 0 10,11 --> 1 10,01 --> change

18 Example 3 cont’d 01,11 --> 0 10,11 --> 1 10,01 --> change

19 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

20 Moore Network for NRZ-to-Manchester

21 Moore Network for NRZ-to-Manchester

22 Mealy Network for NRZ-to-Manchester