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Sequential Circuits

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# Sequential Circuits - PowerPoint PPT Presentation

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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### SequentialCircuits

Design

Inputs

outputlogic

Outputs

next statelogic

Next State

Current State

SequentialCircuits

x

A

Q

D

A

Q

C

B

Q

D

Q\'

C

Clock

y

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

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

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
• Selecttheflip-floptypes. (D flipflop)
• Deriveflip-flopinputequations.

AB

X

AB

X

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

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

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

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

What is the SMD forthisstatediagram?