SEQUENCE DECTOR
Design of the 11011 Sequence Detector
A sequence detector accepts as input a string of bits: either 0 or 1.
Its output goes to 1 when a target sequence has been detected.
There are two basic types: overlap and non-overlap.
In an sequence detector that allows overlap, the final bits of one sequence can be the start of another sequence.
11011 detector with overlap
11011011011
Z
11011 detector with no overlap
X
00001001001
Z
00001000001
Slide 1 of 23 slides
Revised 9/28/2009
Copyright © 2009 by Edward L. Bosworth, Ph.D. All rights reserved.
Chapter 7 Appendix
Design of a 11011 Sequence Detector
Problem: Design a 11011 sequence detector using JK flip-flops. Allow overlap. Step 1 – Derive the State Diagram and State Table for the Problem
Step 1a – Determine the Number of States
We are designing a sequence detector for a 5-bit sequence, so we need 5 states.
We label these states A, B, C, D, and E. State A is the initial state.
Step 1b – Characterize Each State by What has been Input and What is Expected
State
A
Has
--
Awaiting
11011
B
1
1011
C
11
011
D
110
11
E
1101
1
Slide 2 of 23 slides
Revised 9/28/2009
Copyright © 2009 by Edward L. Bosworth, Ph.D. All rights reserved.
Chapter 7 Appendix
Design of a 11011 Sequence Detector
Step 1c – Do the Transitions for the Expected Sequence
Here is a partial drawing of the state diagram. It has only the sequence expected. Note that the diagram returns to state C after a successful detection; the final 11 are used again.
B
1/0
1/0
A
C
1/1
E
0/0
D
1/0
The sequence is 1
Note the labeling of the transitions: X /
Z. Thus the expected transition from A to B has an input of 1 and an output of
0.
The transition from E to C has an output of 1 denoting that the desired sequence has been detected.
1 0 1 1.
Slide 3 of 23 slides
Revised 9/28/2009
Copyright © 2009 by Edward L. Bosworth, Ph.D.
A sequence detector accepts as input a string of bits: either 0 or 1.
Its output goes to 1 when a target sequence has been detected.
There are two basic types: overlap and non-overlap.
In an sequence detector that allows overlap, the final bits of one sequence can be the start of another sequence.
11011 detector with overlap
11011011011
Z
11011 detector with no overlap
X
00001001001
Z
00001000001
Slide 1 of 23 slides
Revised 9/28/2009
Copyright © 2009 by Edward L. Bosworth, Ph.D. All rights reserved.
Chapter 7 Appendix
Design of a 11011 Sequence Detector
Problem: Design a 11011 sequence detector using JK flip-flops. Allow overlap. Step 1 – Derive the State Diagram and State Table for the Problem
Step 1a – Determine the Number of States
We are designing a sequence detector for a 5-bit sequence, so we need 5 states.
We label these states A, B, C, D, and E. State A is the initial state.
Step 1b – Characterize Each State by What has been Input and What is Expected
State
A
Has
--
Awaiting
11011
B
1
1011
C
11
011
D
110
11
E
1101
1
Slide 2 of 23 slides
Revised 9/28/2009
Copyright © 2009 by Edward L. Bosworth, Ph.D. All rights reserved.
Chapter 7 Appendix
Design of a 11011 Sequence Detector
Step 1c – Do the Transitions for the Expected Sequence
Here is a partial drawing of the state diagram. It has only the sequence expected. Note that the diagram returns to state C after a successful detection; the final 11 are used again.
B
1/0
1/0
A
C
1/1
E
0/0
D
1/0
The sequence is 1
Note the labeling of the transitions: X /
Z. Thus the expected transition from A to B has an input of 1 and an output of
0.
The transition from E to C has an output of 1 denoting that the desired sequence has been detected.
1 0 1 1.
Slide 3 of 23 slides
Revised 9/28/2009
Copyright © 2009 by Edward L. Bosworth, Ph.D.