logic design chapter 6
TRANSCRIPT
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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.