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
1
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
2
Design of a Sequence Detector (14.1)
Seq. ends in 101
--> Z=1 (no reset)
otherwise--> Z=0
Convert State Graph
to State Table:
Represent the three
states with
two FF’s A and B
to obtain the transition
table.
3
Design of a Sequence Detector (14.1)
Plot next state and Z
maps from transition
table
4
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 DA = A+, DB = B+
which leads to the network:
5
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
6
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.
7
Mealy Sequential Network (14.2)
Seq. ends in
010 or 1001
--> Z=1
Otherwise
--> Z=0
Partial State Graph
-gives Z=1 for seq. 010
8
Mealy Sequential Network (14.2)
Seq. ends in
010 or 1001
--> Z=1
Otherwise
--> Z=0
Partial State Graph
-additional states for seq. (1001)
9
Mealy Sequential Network (14.2)
Seq. ends in
010 or 1001
--> Z=1
Otherwise
--> Z=0
Final State Graph
-takes into account all other
input sequences
10
Moore Sequential Network (14.2)
Z=1 if total no. of 1’s
received is odd and
at least two
consecutive 0’s rec’d
11
Moore Sequential Network (14.2)
Z=1 if total no. of 1’s
received is odd and
at least two
consecutive 0’s rec’d
12
Guidelines for Construction of State Graphs
13
1
1
Final graph includes other seq.
14
Soln.:
(A blank space above the slash indicates that the network has no other
Input than the clock.)
The repeating part of the sequence is generated using
a loop.
15
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.
16
Example 3 cont’d
We can set up the state table shown
below.
e.g. S4 row:
If 00 rec’d the input seq. has been
10,00 so output does not change and
we go to S0.
If 01 rec’d the input seq. has been
10,01 so output changes to 1 and
we go to S3.
If 11 rec’d the input seq. has been
10,11 so output changes to 1 and
we go to S1.
If 10 rec’d the input seq. has been
10,10 so output does not change and
we stay in S4.
01,11 --> 0
10,11 --> 1
10,01 --> change
17
Example 3 cont’d
01,11 --> 0
10,11 --> 1
10,01 --> change
18
A Converter for Serial Data Transmission:
NRZ-to-Manchester
• 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
19
Moore Network for NRZ-to-Manchester
20
Moore Network for NRZ-to-Manchester
21
Mealy Network for NRZ-to-Manchester
22