IMPLEMENTATION ASSIGNMENT AND CIRCUIT STATE · PDF fileSEQUENTIAL CIRCUITS ANALYSIS,...

Chapter 15

SEQUENTIAL CIRCUITS ANALYSIS, STATE-MINIMIZATION,

ASSIGNMENT AND CIRCUIT IMPLEMENTATION

Ch15L1- "Digital Principles and Design", Raj Kamal, Pearson Education, 2006 2

Lesson 1

General Sequential Circuit with the memory section and combinational circuits at input and output stages


Outline

• Next state of a Flip Flop • General sequential circuit • Synchronous Sequential circuit• Asynchronous sequential circuit • Clocked sequential circuit


Flip-Flop States

• Qn+1 is the next state after the (n + 1)th

transition • Qn is state (present state)


Flip-flop Characteristic expressions for next state

• SR–FF: Qn+1 = S + R. Q n

• D–FF: Qn+1 = D• JK– FF: Qn+1 = J. Q n + K. Q n

• T –FF: Qn+1 = T.Q n + T. Q n

= T. XOR Q n


Outline

• Flip Flops• General sequential circuit • Synchronous Sequential circuit• Asynchronous sequential circuit • Clocked sequential circuit


General Sequential Circuit

• In general, a sequential circuit consist of a complex circuit, which combines memory section and combinational circuit(s)


Memory Section Output Q

• m of flip-flops, which have a set Q with m present state outputs —Q0, Q1… and Qm–1.


External Inputs Xand Present state Q as input to a

combinational circuit

• A Set X of i inputs — X0, X1, ...Xi–1.

• Q are always the inputs to the combinational circuit


Outputs Y from the combinational circuit with Q and X in the inputs

• A Set Y of i outputs — Y0, Y1, ...Yi–1 out of Y0, Y1, ...Yi–1 are feedback as inputs to memory section to get next state.

�Note: Sequential circuit is one the present state Q is input to have transition to next state


General Sequential Circuit

Y0...Yj–1m- FFs Memory Section

Combinational Circuit

Q0

...Qm–1

Q

Present state

Y0

...Yj–1

Next state

FeedbackY0...Yj

YX0...Xi–1

X


Outline

• Flip Flops• General sequential circuit • Synchronous Sequential circuit• Asynchronous sequential circuit • Clocked sequential circuit


Synchronous sequential circuit• Synchronous sequential circuit is a circuit in

which the output Y depends on present state Q and present inputs X at the clocked instances only. These instances can be defined by the clock inputs ↑ or ↓ or or and memory section activates to give next state Q’.


General Synchronous Sequential Circuit

Sequential Circuit

Q0

...Qm–1

Q

Present state

c0...cp–1

Clocking instances

Q

Change to next state Q’ and Y at clock input instances only

YY0...Yj–1X0...Xp–1

External Inputs

X


Outline

• Flip Flops• A general sequential circuit • Synchronous Sequential circuit• Asynchronous sequential circuit • Clocked sequential circuit


Asynchronous sequential circuit• Asynchronous sequential circuit is a circuit

in which not only the present inputs X and present state Q but also the sequences of changes affect the output Y. The changes can be at undefined instances.


General Asynchronous Sequential Circuit

Sequential Circuit

Q0

...Qm–1

Q

Present state

X0...Xp–1

External Inputs

Q

YY0...Yj–1

XChange to next state Q’ and Y at undefined instances


Outline

• Flip Flops• A general sequential circuit • Synchronous Sequential circuit• Asynchronous sequential circuit • Clocked sequential circuit


Clocked Sequential Circuit• A clocked sequential circuit is a

synchronous sequential circuit in which the output Y depends on present state Q and present inputs X at a clocked instance, which are identical to all the flip-flops at the memory section.

�Memory section undergoes change to next state input after the identical clock inputs occur at each flip-flop


General clocked Sequential Circuit

Sequential Circuit

Q0

...Qm–1

Q

Present state

Q

Change to next state Q’ and Y at clock input instances only

YY0...Yj–1X0...Xp–1

External Inputs

X

Clocking instance


Outline

• Flip Flops• A general sequential circuit • Synchronous Sequential circuit• Asynchronous sequential circuit • Clocked sequential circuit• Moore and Mealy Machines


State Machine• A sequential circuit can also be considered

as a machine producing states after undergoing sequential transitions

• Instances of Sequence change can be guided by the clock inputs in synchronous sequential circuits

• Instances of Sequence change is not guided in asynchronous sequential circuits


Clocked Sequential Circuit as Moore Machine



Q0

...Qm–1

QMoore Machine

Present state

Y0

...Yi–1

Next state

FeedbackY0...Yj–1

Y

Clocking instance


Clocked Sequential Circuit as Mealy Machine



Q0

...Qm–1

QMealy Machine

Present state

Y0

...Yj–1

Next state

FeedbackY0...Yj

YX0...Xi–1

X

Clocking instance


Moore Machine• Q’ = FQ (Q) [Next state outputs Q’ are the

function of past state as the present inputsat a clocking instance.] and Y = FQ (Q) [Yis a function of present state outputs Qbefore the clocking instance.]


Mealy Machine • Q’ = FQ (X, Q) [Next state outputs Q’ are

the function of past state Q and present external inputs at a clocking instance.] and Y = Fo (Q) [Y is a function of present state outputs Q before the clocking instance.]


Moore-Mealy Conversion • Any sequential circuit for the Y can be

designed as Mealy machine as a Moore machine can be converted to a Mealy machine by using appropriate set of (X, Q, FQ, FY). Similarly any sequential circuit for the Y can be designed as Moore machine as a Mealy machine can be converted to a Moore machine by using appropriate set of (Q, FQ, FY).


Summary


• Sequential circuit has both the memory section and combinational circuit

• General sequential circuit has external inputs, and present state as the input to generate next state


• Synchronous sequential circuit next state at outputs depends on external inputs, and present state at the clock instances to generate next states

• Clocked sequential circuit next state at outputs depends on external inputs, and present state at a clock instance the input to generate next state


• Asynchronous sequential circuit next state at outputs depends on external inputs, and present state at the undefined instances

• Mealy machine next state outputs Y and Q’ are the function of past state Q and present external inputs at a clocking instance

• Moore machine outputs Y and Q’ are the function of past state Q at a clocking instance


End of Lesson 1 on General Sequential Circuit with the memory section and combinational circuits at input and output stages


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IMPLEMENTATION ASSIGNMENT AND CIRCUIT STATE · PDF fileSEQUENTIAL CIRCUITS ANALYSIS,...

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