State Diagrams Some Examples Design of Sequential Circuits Design Steps Design of Sequence Recognizer (1011) State Diagram State Table State Assignment

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Session 26: Focus
 State Diagrams
◦ Some Examples
 Design of Sequential Circuits
 Design Steps
 Design of Sequence Recognizer (1011)
◦ State Diagram
◦ State Table
◦ State Assignment

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State Diagrams: Some Examples

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Example 1: Find 11 in the Sequence
S0 S1
1 / 1
1 / 0
0 / 0
0 / 0
Output is 1 when two consecutive 1s are found in the sequence:
Input/output
Note: The number of arcs leaving any circle is 2n,
where n is the number of inputs to the sequential circuit.

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Example 2: Find 111 in the Sequence
S0 S1
1 / 0
0 / 0
S2
1 / 1
1 / 0
0 / 0
0 / 0
Output is 1 when three consecutive 1s are found in the sequence:
Corrected S1 to S2 transition
From 1/1 to 1/0

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Design of
Synchronous Sequential Circuits

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Design Steps

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Design Steps Explained …
1. Start with verbal specifications of the problem
2. Derive the state table from it
• In some cases, it is easier to first obtain a state diagram from
the verbal description and then state table
3. Try to minimize number states to get reduced state
table
4. Assign binary codes to the reduced states
 Which is called output or state transition table
5. Derive Flip-flops input equations using flip-flops excitation
tables
 It depends on the choice of flip-flops to be used in the circuit
6. Derive Output equation in terms of inputs and flip-flop outputs
7. Finally, the logic diagram of the sequential circuit is constructed

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Example Design of a
Sequential Circuits

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Step 1: Problem Definition
 Design a sequence recognizer which detects an input
sequence of 1011
 The sequence recognizer outputs a ‘1’ on detecting an
the input sequence (1011).
 The sequential circuit is to be designed using JK and D
type flip-flops
 A sample input/output trace for the sequence detector
is given below:

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Step 2: State Diagram
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 101 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 101 as last three bits
X is Input
Y is Output
Y
State Table in an
Alternative Format
Y

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Step 4: State Assignment
Output is 1 when 1011 pattern is found in the sequence:
01 111000
 It is necessary to replace symbolic names of the states with
binary codes in order to proceed with the design.
 If there are m states, then the codes must contain n bits, where
2n ≥ m, and each state must be assigned an unique code
 The binary numbers from 0 through (2m+n – 1) are listed under
the present-state and input columns.
State Transition Table

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Session 26: Summary
 State Diagrams
◦ Some Examples
 Design of Sequential Circuits
 Design Steps
 Design of Sequence Recognizer (1011)
◦ State Diagram
◦ State Table
◦ State Assignment

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References
Ref 1 Ref 2