2.
OUTLINE
•
Introduction
•
Types of Finite State Machines
•
•
•
Mealy State Machine
Moore State Machine
Example
2
3.
Finite State Machine
• FSMs are different from counters in the sense that they
have external I/Ps, and state transitions are dependent on
these I/Ps and the current state.
• Simple forms of pattern matching.
• Models for sequential logic circuits, of the kind on which
every present-day computer and many device controllers is
based.
3
4.
Mealy and Moore Machines
External I/Ps
External
I/Ps
m1
External O/Ps
m1
Comb.
Logic
n
FFs
m2
Next State
Comb.
Logic
n even
↓
odd
n
Output
Logic
CLK
m2
FFs
n
CLK
External Outputs
Moore Machine Model
Mealy Machine Model
4
5.
Difference Between Mealy and Moore Machine
Mealy
(1) O/Ps depend on the present
state and present I/Ps
(2) The O/P change asyn
-chronously with the
enabling clock edge
(3)
(4)
Moore
O/Ps depend only on the
present state
Since the O/Ps change
when the state changes,
and the state change is
synchronous with the
enabling clock edge, O/Ps
change synchronously
with this clock edge
A counter is a Moore
machine
A counter is not a Mealy
machine
A Mealy machine will have
the same # or fewer states
than a Moore machine
5
6.
Finite State Machine (FSM) Design
Example:
There is a one bit-serial I/P line. Design an FSM that outputs a ‘0’ if an
even # of 1’s have been received on the I/P line and the outputs a ‘1’
otherwise.
x
FSM
O/p y
CLK
CLK
x
# of
1s
even
(0)
odd
(1)
even
(2)
odd
(3)
6
odd
(3)
7.
Solution 1: (Mealy)
Solution 2: (Moore)
0
0/0
Reset
Even
Transition
Arc
Input
1/1
1/0
Odd
Reset
Output
Even
Output
[0]
O/P is dependent
on current state and
input in Mealy
1
1
Odd
[1]
0
0/1
Mealy Machine: Output is associated
with the state transition, and appears
before the state transition is completed
(by the next clock pulse).
Input
Output is
dependent only
on current state
Moore Machine: Output is associated
with the state and hence appears
after the state transition take place.
7
8.
State Transition Table
(Even-Parity Checker)
Even State: 0 ;
Present
State
Input
A
Odd State: 1;
Next
State
x
State Variable A
Mealy
O/P
Moore
O/P
A+
y1
D-FF
Excit.
y2
DA
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1x
1
0
Input variables
to comb. logic
1
1
DA= A⊕x ;
y1 = A for Moore
y2 = A⊕x for Mealy
Output functions 1
1
y2
0
N.S. & O/P
Logic
Q
A FF
x
N.S.
Logic
Or
Q
DA
CLK
8
0
A
O/P
Logic
FFs
y1
DA
9.
Moore M/C Implementation
a) D-FF
0
D
x=1
R
CLK
A
Q
y1
Q
Reset
Moore O/P is synchronized with clock.
Mealy M/C Implementation
y2
0
1
D
x=1
CLK
Q
R
A
Q
Reset
a) D-FF
Mealy O/P is not synchronized with clock.
9
10.
Moore M/C Implementation
a) D-FF
0
D
x=1
R
CLK
A
Q
y1
Q
Reset
Moore O/P is synchronized with clock.
Mealy M/C Implementation
y2
0
1
D
x=1
CLK
Q
R
A
Q
Reset
a) D-FF
Mealy O/P is not synchronized with clock.
9
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