A Sequential Parity Checker
X
(Data Input)
Parity
Checker
Z
Clock(P)
Odd Parity –
Total number of 1 bits is odd.
Even Parity –
Total number of 1 bits is even.
Example: Odd parity
7 data bits parity bit
This is a simple example of a
sequential network with one input
plus clock.
0000000
0110110
1010101
1
0
1
Designed for serial data input
-- data enters the network sequentially,one bit at a time.
For an odd parity checker, Z = 1 (at a given time) if the total number
of 1’s received is odd.
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A Sequential Parity Checker
State Encoding:
State Graph
State Table
Network
S0  Q = 0
S1  Q = 1
State Table for T-FF implementation
Timing Diagram
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Moore Sequential Network
-a sequential network whose
output is a function of the
present state only.
X=10101
A=011110
B=011001
Z = (0) 1 1 0 0 1
3
Mealy Sequential Network
-a sequential network
whose output is a
function of both the
present state and
the input.
X=10101
A=000110
B=011110
Z = 1(0)1 0(1)0 1
A “false” value arises because
the network has assumed a new
state but the old input associated
with the previous state is still
present.
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Deriving the State Table
1. Determine the FF input equations and the output equations
from the network.
2. Derive the next-state equation for each FF from its input
equations using the characteristic equation
D FF Q+ = D
T-FF Q+ = T  Q
SR-FF Q+ = S + R’Q
JK-FF Q+ = JQ’ + K’Q
3. Plot a next state map for each FF
4. Combine these maps to form the state table.
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Moore Sequential Network
The FF input eqns. and output eqn. are
JA = X
JB = X
KA = XB’ Z = B
KB = X  A’
The next state eqns. for the FF’s are
A+ = JAA’ + K’AA = XA’ + (X’ + B)A
B+ = JB B’ + K’BB = XB’ + (X A’)’B = XB’+(XA’+ X’A)B
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Moore Sequential Network
Moore State Graph
Moore State Tables
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Mealy Sequential Network
The next-state and output eqns. are
8
Mealy Sequential Network
input/output
Mealy State Graph
Mealy State Tables
9
Mealy Sequential
Network
-- Another Example
-two inputs and two
outputs
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Mealy Sequential
Network -- General
Model D-FF’s
Combinational subnetwork
realizes the n output
functions and the k next
state functions, which serve
as inputs to the D=FF’s.
All FF’s change state
synchronous with clock pulse.
After FF’s change state the
new FF outputs are fed back
into the combinational
subnetwork awaiting the next
clock pulse.
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Moore Sequential
Network -- General
Model D-FF’s
-Similar to Mealy.
In the combinational
subnetwork the output section
is drawn separately from the
input section. (Output is only
a function of the present state.)
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State Table with Multiple Inputs and Outputs
Let X=0 rep. the input combination X1X2= 00, X=1 rep. X1X2= 01, etc.
Let Z=0 rep. the output combination Z1Z2= 00, Z=1 rep. Z1Z2= 01, etc.
Obtain the following table in terms of a single input variable X and a single
output variable Z.
d(S0 , 1) = S2
l(S0 , 1) = 2
d(S2 , 3) = S1 Next State functions … S+ = d(S,X)
l(S2 , 3) = 1
Output function …….. Z = l(S,X)
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What do you have to know?
• Analysis of clocked sequential networks
• State Graph, State Table, Network
Realization
• Timing Diagrams
• Deriving State Table
• Moore and Mealy State machines
• General Models for Sequential Networks
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