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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 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

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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