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Sequential Circuits. Design. Inputs. output logic. Outputs. next state logic. Next State. Current State. Sequential Circuits. x. A. Q. D. A. Q. C. B. Q. D. Q'. C. C lock. y. Design Example : Sequence Recognizer.

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Sequential circuits

SequentialCircuits

Design


Sequential circuits1

Inputs

outputlogic

Outputs

next statelogic

Next State

Current State

SequentialCircuits

x

A

Q

D

A

Q

C

B

Q

D

Q'

C

Clock

y


Design example sequence recognizer
DesignExample: SequenceRecognizer

  • A sequential circuit that recognizes the occurrencethe bit sequence 1101 (The sequence 1101 must be recognized each time it occurs in the input sequence.)

    • Thus, the sequential machine must remember that the first two one's have occurred as it receives another symbol.

  • Input: X(t)  {0, 1} Output: Z(t)  {0, 1}

Time 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

X(t) 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1

Z(t) 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1


Obtain the state diagran

S1

S2

S3

ObtainTheStateDiagran

Time 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

X(t) 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1

Z(t) 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1

1/1

1/0

0/0

1/0

S0

1/0

0/0

0/0

0/0

A Mealy Machine


Obtain state table
ObtainState Table

1/1

  • From the State Diagram, we can fill in the State Table.

    • Assignbinarycodesforthestates

1/0

0/0

1/0

00

01

10

11

1/0

0/0

0/0

0/0


Find flip flop input and output equations
Find Flip-Flop Input and Output Equations

  • Selecttheflip-floptypes. (D flipflop)

  • Deriveflip-flopinputequations.

AB

X

AB

X


Draw logic diagram

X

Z

DrawLogicDiagram

Clock


One flip flop per state one hot assignment
One Flip-flop per State (One-Hot) Assignment

1/1

1/0

0/0

1/0

0001

0010

1000

0100

  • Provides simplified analysis and design

  • Combinational logic may be simpler, but flip-flop cost higher

1/0

0/0

0/0

0/0


Design example modulo 3 accumulator for 2 bit operands

00

A/00

B/01

C/10

DesignExample: modulo 3 accumulator for 2-bit operands

  • It adds each input operand to the stored sum, which is initially 0. Thentakesthemodulo.

  • (2 + 0) modulo 3 = 2, (1+2) modulo 3 = 0 …

  • Stored sum: (Y1,Y0), Input: (X1,X0), Output: (Z1,Z0)

  • Reset

    MealyorMoore?

    01


    The state machine diagram model smd

    A×B

    A×B

    S0

    S1

    S0

    S1

    A + B

    A + B

    Y, Z

    A/Y, B/Z

    S2

    S2

    TCI Outputs

    Moore Outputs

    C/Y

    A×B/Y

    A×B

    S0

    S1

    S0

    S1

    C/Y

    (A + B)/Z

    (A + B)

    S2

    S2

    TCD Outputs

    The State Machine Diagram Model (SMD)

    • Input Variables A, B, COutput Variables Y, ZDefault: Y = 0, Z = 0

    Transition condition (TC)

    Transition condition-independent (TCI)

    Transition condition-dependent (TCD)

    Transition andoutputcondition-dependent (TCOD)

    TCOD Outputs


    Example 1
    Example-1

    Defaults: Y = 0, Z = 0

    Y, Z

    A/Y, B/Z

    A×B

    S0

    S1

    A + B

    BC

    A×C

    A/Z

    A + C

    B×C

    A/Y

    (B + C)/Z

    S2

    S3

    B×C/Y

    What is thestatetableforthis SMD?


    Example 2
    Example-2

    What is the SMD forthisstatediagram?


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