Search for notes by fellow students, in your own course and all over the country.
Browse our notes for titles which look like what you need, you can preview any of the notes via a sample of the contents. After you're happy these are the notes you're after simply pop them into your shopping cart.
Title: Sequential machine design
Description: Detail about Sequential machine design
Description: Detail about Sequential machine design
Document Preview
Extracts from the notes are below, to see the PDF you'll receive please use the links above
Design problem normally starts with a word description of input output
relation and ends with a circuit diagram having sequential and
combinatorial logic elements
...
Design a digital circuit whose outputs are to take on specific values after
a specific sequence of inputs has taken place
...
These problems are non-issues in synchronous circuit where
external clock trigger arrives after all the inputs are stabilized
...
66
Two states are equivalent if they have the same output and go to the same
(equivalent) next states for each possible input
Removal of redundant states will reduce the amount of logic required and
hence reduce the no
...
In Moore model circuit outputs, also called primary outputs are
generated solely from secondary outputs or memory values
...
99
MOORE MODEL
MEALY MODEL
The output depends only on present
state and not on input
The output is derived from present
state as well as input
It requires more number of states and
thereby more hardware to solve any
problem
It requires less number of states and
thereby less hardware to solve any
problem
The output is generated one clock cycle
after
...
The glitches occurs
10
10
A Sequence Recognizer is a special kind of sequential circuit that looks
for a special bit pattern in some input
The recognizer circuit has only one input, X
One bit of input is supplied on every clock cycle
There is one output Z, which is 1 when the desired pattern is found
Our example will detect the bit pattern “1001”:
Inputs:
X
1 10 0 11 0 1 0 01 0 01 1 0 …
Outputs: Z
0 00 0 10 0 0 0 01 0 01 0 0 …
A sequential circuit is required because the circuit has to “remember”
the inputs from previous clock cycles, in order to determine whether
or not a match was found
11
11
Step: 1 State diagram
*Note
0/0
A
X= 1001
Z= 0001
present
state
1/0
1/0
B
1/0
1/1
0/0
0/0
A
B
C
D
0/0
1/0
0/0
0/0
input/
output
C
0/0
next
state
D
12
12
Step: 2 Assigning binary codes to States
• We have four states ABCD, so we need at least two flip-flops Q1Q0
...
Present state
Present
state
Next state
Next state
Output
Q1
X=0
X=1
X=0
X=1
A
A
B
0
0
B
C
B
0
0
C
D
B
0
0
D
A
B
0
1
Q0
X=0
X=1
Q1
Q0
Q1
Q0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
13
13
Step: 3 Finding flip-flop input values
Transition table of JK flip flop
QP
QN
J
K
0
0
0
X
0
1
1
X
1
0
X
1
1
1
X
0
14
14
Step: 4 Find equations for the FF inputs and output
QP0
QN0
J0
K0
X
0
1
1
X
X
1
1
1
X
0
1
1
X
0
1
1
X
0
X
1
1
1
X
0
Q1 Q0
X
00
01
11
10
0
X
X
1
1
X
X
1
For J0 and K0
When X=0
0
1
QP 0
QN0
J0
K0
0
0
0
1
0
0
1
J0 = X+Q1
When X=1
X
Q1 Q0
00
0
1
01
11
10
X
1
1
X
X
0
0
X
K0 = X’
15
15
Step: 4 Find equations for the FF inputs and output
QP1
For J1 and K1
When X=0
QN1
J1
K1
QP1
QN1
J1
K1
When X=1
0
0
0
X
0
0
0
X
0
1
1
X
0
0
0
X
1
1
X
0
1
0
X
1
1
0
X
1
1
0
X
1
Q1 Q0
X
00
01
11
10
Q1 Q0
X
00
01
11
10
0
1
X
X
0
0
X
X
0
1
0
1
J1 = X’Q0
X
X
1
0
X
X
1
1
K1 = X+Q0
16
16
Step: 5 Build the circuit
For Output Z
K-map
Q1 Q0
00
X
0
0
0
0
0
0
0
1
0
1
01
Z = XQ1Q0
11
10
J1 = X’ Q0
K1 = X + Q0
J0 = X + Q1
K0 = X’
17
17
Building the same circuit with D flip-flops
• We already have the state table and state assignments, so we can
just start from Step 3, finding the flip-flop input values
Step: 3 Finding flip-flop input values
Transition table of D flip flop
QP
QN
D
0
0
0
0
1
1
1
0
0
1
1
1
18
18
Step: 4 Find equations for the FF inputs and output
For D0
When X=0
QP0
QN0
D0
QP0
QN0
D0
When X=1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
X
Q1 Q0
0
1
00
01
11
10
0
0
0
1
1
1
1
1
D0 = X+Q1Q0’
19
19
Step: 4 Find equations for the FF inputs and output
For D1
When X=0
QP 0
QN 0
D0
QP0
QN0
D0
When X=1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
X
Q1 Q0
0
1
00
01
11
10
0
1
0
1
0
0
0
0
D1 = X’Q1’Q0 + X’Q1Q0’
20
20
Step: 5 Build the circuit
For Output Z
K-map
Q1 Q0
00
X
0
0
0
0
0
0
0
1
0
1
01
11
10
Z = XQ1Q0
D1 = Q1 Q0’ X’ + Q1’ Q0 X’
D0 = X + Q1 Q0’
21
21
Design a circuit of sequential machine using T-flipflop, whose output is 1
whenever pattern is 010
Step: 1 State diagram
A
1/0
0/0
A
B
C
1/0
0/0
1/0
B
0/0
1/0
0/1
C
1/0
22
22
Step: 2 Assigning binary codes to States
Present
Next
X=1
X=0
Output
X=1
X=0
A
B
A
0
0
B
B
C
0
0
C
B
A
1
0
Next State Table
Put A=00
B=01
C=10
Present
Next
X=0
Q1
0
0
1
Q0
0
1
0
Q1
0
0
0
X=1
Q0
1
1
1
Q1
0
1
0
Q0
0
0
0
23
23
Step: 3 Finding flip-flop input values
Transition table of T flip flop
QP
QN
T
0
0
0
0
1
1
1
0
1
1
1
0
24
24
Step: 4 Find equations for the FF inputs and output
QP0
X=0
QN0
T0
QP0
X=1
QN0
T0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
00
01
11
10
1
0
0
1
x
X
K-map for T0
Q1Q0
x
0
1
1
0
T0=X’Q0’+XQ0
25
25
Step: 4 Find equations for the FF inputs and output
X=0
K-map for T1
Q1Q0
x
0
1
QP1
QN1
T1
QP1
X=1
QN1
T1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
00
01
11
0
0
0
1
x
X
10
1
1
T1=Q1+XQ0
26
26
Step: 5 Build the circuit
T0=X xnor Q0
For Output Z
K-map
X
Q1 Q0
0
1
00
01
0
0
x
1
0
0
x
0
Z = X’Q1
11
10
T0=X’Q0’+XQ0
T0=X xnor Q0
T1=Q1+XQ0
T1=Q1+XQ0
Z = X’Q1
Design a circuit of sequential machine using T-flipflop, whose output is 0
whenever pattern is 101
Step: 1 State diagram
0/1
A
1/1
B
1/1
0/1
1/0
C
28
28
Step: 2 Assigning binary codes to States
Present
Next
X=1
X=0
Output
X=1
X=0
A
A
B
1
1
B
C
B
1
1
C
A
B
1
0
Next State Table
Put A=00
B=01
C=10
Present
Next
X=0
Q1
0
0
1
Q0
0
1
0
Q1
0
1
0
X=1
Q0
0
0
0
Q1
0
0
0
Q0
1
1
1
29
29
Step: 3 Finding flip-flop input values
Transition table of T flip flop
QP
QN
T
0
0
0
0
1
1
1
0
1
1
1
0
30
30
Step: 4 Find equations for the FF inputs and output
QP0
X=0
QN0
T0
QP0
X=1
QN0
T0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
00
01
11
10
0
1
1
0
x
X
K-map for T0
Q1Q0
x
0
1
0
1
T0=X’Q0+XQ’0
31
31
Step: 4 Find equations for the FF inputs and output
X=0
K-map for T1
Q1Q0
x
0
1
QP1
QN1
T1
QP1
X=1
QN1
T1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
00
01
11
0
0
1
0
x
X
10
1
1
T1=Q1+X’Q0
32
32
Step: 5 Build the circuit
T0=X xor Q0
For Output Z
K-map
X
Q1 Q0
0
1
00
01
1
1
x
1
1
1
x
0
Z = X’+Q’1
11
10
T0=X’Q0+XQ’0
T0=X xor Q0
T1=Q1+X’Q0
T1=Q1+X’Q0
Z = X’+Q’1
State diagram for 1101: Output 1 if the sequence 1101 has been read, output 0
otherwise
...
Mealy
Model
A
0/0
Moore
Model
0
A/0
1
1/0
B/0
0
1
B
0/0
C/0
1/0
0
0/1
C
1
1/0
0
D/1
1
3/10/2013
sequence
recognizer
Hope it helped
you!!
Hope it helped you!!!
Title: Sequential machine design
Description: Detail about Sequential machine design
Description: Detail about Sequential machine design