The document outlines the design of a sequence recognizer for the input sequence '1001' using JK flip-flops. It details the steps involved including problem definition, state diagram creation, state table generation, state assignments, and the design of combinational circuits. Additionally, it includes a summary and references for further study.

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Session 29: Focus
 Design of Sequence Recognizer (1001)
◦ State Diagram
◦ State Table
◦ State Assignment
◦ State Transition Table
◦ Designing combinational circuit
◦ Circuit Diagram – Home work

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Design of Sequence Detector (1001)

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Step 1: Problem Definition
 Design a sequence recognizer which detects an input sequence
of 1001
 The sequential circuit is to be designed using only JK flip-
flops
 The sequence recognizer outputs a ‘1’ on detecting the input
sequence (1001).
◦ Note that the last four bits need to be 1001 for the output to be 1
◦ Every four clock cycles the output will be one, if the following
sequence is input to the circuit (100110011001 …)
◦ Every three clock cycles after the first pattern is detected, if the input
is (1001001001001 …)

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Step 2: State Diagram
Output is 1 when 1001 pattern is found in the sequence:
State S0: Initial state
S1: Last single bit of the sequence was 1
S2: Detection of sequence 10 as last two bits
S3: Detection of sequence 100 as last three bits

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Step 3: State Table
Output is 1 when 1011 pattern is found in the sequence:
State S0: Initial state
S1: Last single bit of the sequence was 1
S2: Detection of sequence 10 as last two bits
S3: Detection of sequence 100 as last three bits
X is Input
Y is Output
Y
State Table in an
Alternative Format
Y
0
0
0
0
0
0
0
1
S0
S1
S2
S1
S3
S1
S0
S1

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Step 4: State Assignment
Output is 1 when 1001 pattern is found in the sequence:
 It is necessary to replace symbolic names of the states with
binary codes in order to proceed with the design.
 So that Flip-flops can be used to maintain the states of the
machine
 For this design we need two JK flip-flops since there are four
states are to be maintained by the machine
State Transition Table

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Output of Step 4: State Transition Table
State Transition Table
Name the States as A B
which are maintained by
Two JK flip-flops
named as A and B
0
0
0
0
0
0
0
1
S0
S1
S2
S1
S3
S1
S0
S1
Y
00
01
10
01
11
01
00
01
0
0
0
0
0
0
0
1

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General Structure of Sequence Detector
 Circuit would have:
◦ Input (X)
◦ Output (Y)
◦ JK Flip-flops – 2 nos.
◦ Clock
◦ Combination circuits
◦ Output of combination circuits
driving the inputs of flip-flops
◦ Flip-flop’s outputs feeding
back into combinational
circuit
J
K
J
K
B
A
Q
Q
B
A
JB
KB
JA
KA

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Deriving the Excitation Table
B
KB
JB
B
KA
JA
A
A
Next
State
Out
put
JA KA JB KB
0 X
0 X
1 X
0 X
X 0
X 1
X 1
X 1
0 X
1 X
X 1
X 0
1 X
1 X
X 1
X 0
Check the flip-flop excitation inputs for the state transitions

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Designing the Combinational Circuits
For designing the actual circuitry for the
combinational circuit, we need to simplify
the excitation table entries, for each inputs
to the flip-flops and output (Y)
JA= BX’ KA = X + B
JB = A + X
Output: Y = ABX
KB = X’
Construct K-maps and verify the
above Boolean expressions
Constructing the circuit diagram: Home work

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Session 29: Summary
 Design of Sequence Recognizer (1001)
◦ State Diagram
◦ State Table
◦ State Assignment
◦ State Transition Table
◦ Designing combinational circuit
◦ Circuit Diagram – Home work

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References
Ref 1 Ref 2