Logic Design Chapter 6

8/12/2019 Logic Design Chapter 6

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Chapter -6

LOGIC DESIGN

SYNCHRONOUS SEQUENTIAL NETWORKS

Definition :

In sequential networks, the outputs are function of present state and present external

inputs. Present state simply called as states or past history of circuit. The existing inputs

and present state for sequential circuit determines next state of networks.

Model of Sequential Network

Types of Sequential Network :

. Asynchronous Sequential Network : The changes in circuit depends on changes

in inputs depending on present state. !ut the change in memory state is not at

gi"en instant of time #ut depending on input.

$. Synchronous Sequential Network : %utput depends on present state and present

inputs at a gi"en instant of time. So timing sequence is required. So memory is

allowed to store the changes at gi"en instant of time.

Structure and Operation of Clocked Synchronous Sequential Circuit :

In synchronous sequential circuit, the network #eha"ior is defined at specific

instant of time associated with special timing. There is master clock which is common to

all &&s that is used in memory element. Such circuits are called as clocked synchronous

sequential circuit.

CombinationalLogic Circuit

Memory

Outputsinputs

PS

NS


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Clock : 'lock is periodic wa"eform with one positi"e edge and one negati"e edge during

each period.

This clock is used for network synchroni(ation

Basic Operation of Clocked Synchronous Sequential Circuit

) indicates all present state of &&.

)* indicates next state of && in network.

+ indicates all external inputs.

)* f-x,) This is next state of network.

/ indicates output signal of sequential networks.

/ g-+,)

The structure shown in gi"en figure is called as Mealy Model or Mealy Machine.

1 0

t

+ ve edge - ve edge


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o!ic Dia!ra" for Moore Network

Transition #quations :To con"ert excitation expression into next state expression, it is necessary to use the

characteristic equations of flip0flops.

The characteristic equations of && depends on types of && used.

1x 2 &or 3 && )* 3

&or 45 &&

&or T && )* T )

!y su#stituting the excitation expressions for a && into characteristic equation, an

alge#raic description of next state of && is o#tained.

The expression for next state in terms of && inputs are referred as transition equations.

)* 3 and )$* 3$

$$

$

$$$

andyxx

and

and

QyyxKQQJ

yxQKyJ

QQZQQZ

+=+=

+==

+==

QKQJQ +=+

$$

$$

QQQxQ

QQQxQ

+=

+=

+

+


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&or Moore network

!y su#stituting the "alues of 4 6 5 inputs we get next state in terms of && present state

and external input.

Transition Tables :

Instead of using alge#raic equations for next state and outputs of sequential

network, it is more con"enient and useful to express the information in ta#ular form.

The Transition Ta#le or State Transition Ta#le or State Ta#le is the ta#ular representation

of the transition and output equations. This ta#le consist of Present State, Next State,

external inputs and output "aria#les. If there are n state "aria#les then $n rows are present

in state ta#le.

State "achine notations :

7 Input 8aria#les 2 1xternal input "aria#les to sequential machine as inputs.

7 %utput 8aria#les 2 9ll "aria#les that exit from the sequential machine are output

"aria#les.

7 State 2 State of sequential machine is defined #y the content of memory, when

memory is reali(ed #y using &&s.

7 Present State 2 The status of all state "aria#le i.e. content of && for gi"en instant of

time t is called as present state.

7 Next State 2 The state of memory at t* is called as Next state.

7 State 3iagram 2 State diagram is graphical representation of state "aria#les

represented #y circle. The connection #etween two states represented #y li"es

with arrows and also indicates the excitation input and related outputs.

7 %utput 8aria#les 2 9ll "aria#les that exit from the sequential machine are output

"aria#les.

$$$$

QKQJQ

QKQJQ

+=

+=

+

+


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PS NS && input

) )* 4 5

: : : +

: +

: +

+ :

B1

0

!011"10

!1#0

11"01

State diagram o$ %-& ''

PS NS && i;p

) )* S <

: : : +

: :

: :

+ :

State diagram o$ S( ''

0 101

00

10

01

0010

9 lication Ta#le of 45 &&


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Transition table for Mealy Network

PS NS && i;p

) )* 3 i;p

: : :

: : :

State diagram o$ ) ''

0 1

01

0

1

PS NS && i;p

) )* T i;p

: : :

:

:

:

State diagram o$ * ''

0 1

01

1

0

9 lication Ta#le of 3 &&

9pplication Ta#le of &&


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Transition table for Moore Network

PS -))$ Next State -)*)$*

Inputs -xy

%utput

-//$

:: : :

:: :: : : :

: : :: ::

: : : :: ::

:: : :: :

Synchronous Sequential 'ircuit

xQQQxZ

QQQQxQ

QQQQxQ

$

$$$$

$$

3,

3,

+=

=+=

=+=

++

++

,,yxx,

,,

$$$

$$$

QyyxKQQJyxQK

yJQQZQQZ

+=+=+=

=+==

$$

$$$$$

$$

x,

),

),

QZQxZ

TQQQxT

TQQQxQT

==

=+=

=+=

+

+


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State Tables :State ta#le consist of PS, NS and output section. The PS and NS of state ta#les are

o#tained #y replacing the #inary code for each in the transition ta#le #y newly defined

sym#ol. The output section is identical to output section of transition ta#le.

Sym#ols for state can #e S, S$, S=,>>Sn or 9, !, ', 3, 1>.

State table for Mealy Machine

PS NS

x : x

%;p /

x : x

:: ? 9 ' ! :

: ? ! 3 3 : :

: ? ' ' 9 :

? 3 9 9 :

State Dia!ra" :

It is graphical representation of state ta#les. 1ach state of network is represented #y

la#eled node.

3irected #ranches connect the nodes to indicate transition #etween states. The directed

#ranches are la#eled according to the "alues of external input "aria#le that permit

transition. The output of sequential network is also entered in state diagram. In case of

Moore Network state diagram, the "alues of input for output is not written.


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State diagram for Mealy Network

State diagram for Moore Network


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Analysis of Synchronous Circuit

The gi"en circuit in a#o"e figure is Mealy Network and the output is function of input

"aria#le and PS of &&. The analysis of a#o"e circuit is as follows.

The #%citation and Output &unction

!y su#stituting the && inputs in characteristic equation, the next state of && is o#tained in

terms of PS of && and external input.

The characteristic equation of 45 && is

The #%citation Table

PS

)$ )-y$ y

1xcitation input

4$ 5$ 4 5x:, x:,

%utput /

x:, x

: : : :

: : : : :

: : :

: : $ :

$$$$

$$

,,, yKyJxKxJ

yxyyyxZ

====

++=

QKQJQ +=+

$$$$$

$

xQKQJQ

QQKQJQ

=+=

=+=

+

+

$

$$$$

$$$$

,,:

,,

,

xWhenandyyzxWhen

yxyyyxZxKxJ

QyKQyJ

=+==

++===

====


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State Table

PS NS %;p /

x : x

)$

-y$

)

-y

state )$* )* state )$* )* state +: +

: : 9 : : 9 : '

: ! : : 9 : ' : :

: ' : ! 3

3 : ! 3 :

State Dia!ra" of Mealy Network

)

C

B

0"1

0"0

0"1

1"0

1"1

0"1

1"11"0

)* )$ y$

)$* x

$

,

,:

yzxif

yyzxif

==

+==

9, !, ', 3 are

Present states.


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Analysis of Moore Network

State Table ' Transition Table

PS NS %;p /

x : x

) )$ State )* )$* State )* )$* state

: : 9 : : 9 : ! :

: ! 3 : : 9

: ' : : 9 : : 9

3 : ' : : 9

$$

$$$

$

$$$$

)6:,

)6,:

,

QDDxif

QDQDxif

QQZ

QQxQQxDQxD

===

===

+=

+==

)* 3

)$* 3$/ ) * )$

$$

$$$

)6:,

)6,:

QDDxif

QDQDxif

===

===


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State Dia!ra" of Moore Network

Analysis of Sequential Network

)1

0

B1

C

1

0

1

0

0

0

01

1

9, !, ', 3 arePresent states.

AxKJ

BKBJBAxy

BB

AA

==

=== ,,


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State Table

PS NS %;p y

x : x

)9 )! state )9* )!* state )9* )!* state x: x

: : S: : S : : S: :

: S : S$ S= :

: S$ : S : S$ :

S= : S$ : S :

State Dia!ra" of Mealy Network

S0

1"1

0"0

0"1

1"1

1"0

S S

1

S,

0"0

0"1

1"0

AB,

AB,:

A.B-,

BAB

BAB

BABBA

QQQxif

QQQxif

QQxQQQ

==

==

==

+

+

++

S:, S, S$, S= are Present

states.

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Logic Design Chapter 6