Design of Sequential Circuits Design Steps Design of Sequence Recognizer (1011) State Diagram State Table State Assignment State Transition Table Designing combinational circuit Circuit Diagram

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Session 27: Focus
 Design of Sequential Circuits
 Design Steps
 Design of Sequence Recognizer (1011)
◦ State Diagram
◦ State Table
◦ State Assignment
◦ State Transition Table
◦ Designing combinational circuit
◦ Circuit Diagram

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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:
Output

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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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Output of Step 4: State Transition Table
State Table
State Transition Table
Name the States as A and B

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General Structure of Sequence Detector
 Circuit would have:
◦ Input (X)
◦ Output (Y)
◦ D Flip-flop
◦ JK Flip-flop
◦ Clock
◦ Combination circuits
◦ Output of combination circuits
driving the inputs of flip-flops
◦ Flip-flop’s outputs feeding
back into combinational
circuit

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Deriving the Excitation Table
Next
State
Out
put
DB
KA
JA

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Designing the Combinational Circuits
Next
State
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 = BX + B’X’
DB = X
Y = ABX

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Final Design of Sequence Detector (1011)
JA = BX’
KA =
DB = X
Y = ABX
BX + B’X’

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Session 27: Summary
 Design of Sequential Circuits
 Design Steps
 Design of Sequence Recognizer (1011)
◦ State Diagram
◦ State Table
◦ State Assignment
◦ State Transition Table
◦ Designing combinational circuit
◦ Circuit Diagram

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References
Ref 1 Ref 2