1. A Sequential Parity Checker
Odd Parity –
Total number of 1 bits is odd.
Even Parity –
Total number of 1 bits is even.
Parity
Checker X Z
(Data Input)
Clock(P)
Example: Odd parity
7 data bits parity bit
This is a simple example of a
sequential network with one input
plus clock.
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.

2. A Sequential Parity Checker
State Encoding:
S0  Q = 0
S1  Q = 1
State Graph
State Table for T-FF implementation
State Table
Timing Diagram
Network

3. Moore Sequential Network
-a sequential network whose
output is a function of the
present state only.
X =
A =
B =
Z = (0)

4. Mealy Sequential Network
-a sequential network
whose output is a
function of both the
present state and
the input.
X =
A =
B =
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.

5. 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.

6. Moore Sequential Network
The FF input eqns. and output eqn. are
JA = X KA = XB’ Z = B
JB = X 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

7. Moore Sequential Network
Moore State Graph
Moore State Tables

8. Mealy Sequential Network
The next-state and output eqns. are

9. Mealy Sequential Network
input/output
Mealy State Graph
Mealy State Tables

10. Mealy Sequential Network
-- Another Example
-two inputs and two
outputs

11. 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.

12. 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.)

13. 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) = S d(S2 , 3) = S1 Next State functions … S+ = d(S,X)
l(S0 , 1) = l(S2 , 3) = Output function …….. Z = l(S,X)

14. 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