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Information on finite state machines (fsms), focusing on mealy and moore machines. Fsms have external inputs and state transitions depend on these inputs and the current state. How to determine states of an fsm, the difference between mealy and moore machines, and examples of their implementation. It also covers interacting fsms.
Typology: Study notes
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Department of Electrical and Computer Engineering
University of Illinois, Chicago
Phone: (312) 355-1314: e-mail: [email protected]
URL: http://www.eecs.uic.edu/~dutt
2
- 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.
- Example : Problem Statement
There is a 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.
combinational ckt?
past inputs in order to solve the problem
Note : If a +ve edge triggerred synchronous sequential circuit is being designed,
the counting of the # of 1s (i.e., the sampling of the
input(s), for a general FSM) occurs T log
ff
su
time
before every +ve edge.
CLK
CLK
Tlog
+Tff
+T su
T log
= comb. logic delay
T ff
= FF delay
Tsu = FF setup time
4
Determining a Reset State:
reset state. E.g., in the parity detector problem, the even state qualifies to be the reset
state, as in the reset state no i/ps recvd zero 1’s recvd even # of 1’s recvd it can
be the even state
this state to the other states (depending on the problem solved by the FSM).
Solution 1: (Mealy)
Even
Odd
0/
Reset
Even
Reset
[0]
Odd
[1]
Output
Input
Output
Input
Transition
Arc
Output is
dependent only
on current state
O/P is dependent
on current state and
input in Mealy
Solution 2: (Moore)
Mealy Machine: Output is associated
with the state transition, and appears
before the state transition is completed
(by the next clock pulse).
Moore Machine: Output is associated
with the state and hence appears
after the state transition take place.
5
FFs
External I/Ps External O/Ps
m 1
m 2
n n
Comb.
Logic
CLK
FFs
n
CLK
n
Output
Logic
m 2
Next State
Comb.
Logic
m 1
External
I/Ps
External Outputs
even
odd
Time t : Even I/P = propagation delay of logic of Mealy M/C
t
t+ t+T CLK
t+T CLK
+ 2
Even
x=
O/P=
O/P=
(Mealy)
Odd O/P=
(Moore)
2
= propagation delay of O/P
logic unit of Moore M/C
7
State=
Even
State=
Odd
Reset 0
State=
Even
Reset
[0]
State=
Odd
[1]
x
FF
N.S.
Logic
CLK
Q
Q D
D-
Assume single bit state information stored in a D-FF
CLK
x
(state)
y 2
(Mealy O/P)
y 1
Moore O/P)
State Transition
is occurring
State Transition
is occurring
S.T. is complete.
S.T. is complete.
odd^ odd
even even even odd
0/
8
D Q
R Q CLK
y 1
x=
A
0
a) D-FF
T Q
R Q
A y 2
x
CLK
b) T-FF
Moore O/P is synchronized with clock.
D Q
R Q CLK
y 2
x=
A
0 1 T Q
R Q
x
CLK
y 1
a) D-FF
b) T-FF
Mealy O/P is not synchronized with clock.
Reset
Reset
Reset
Reset
A
= Ax ; T A
= x
y 1
= A for Moore; y 2
= Ax for Mealy
10
Here is how the control is supposed to work. The vending machine delivers
a package of gum after it has received 15 cents in coins. The machine has a single
coin slot that accepts nickels and dimes, one coin at a time. A mechanical sensor
indicates to the control whether a dime or a nickel has been inserted into the coin slot.
The controller’s output causes a single package of gum to be released down a chute
to the customer.
One further specification: We will design our machine so it does not give
change. A customer who pays with two dimes is out 5 cents!
Vending
Machine
FSM
CLK
Reset
Coin
Sensor
Gum
Release
Mechanism
Open
Vending Machine block diagram
States:
11
— The figure below show the Moore and Mealy machine state transition diagrams.
0 cent
[0]
5 cent
[0]
10 cent
[0]
=15 cent
[1]
Moore machine
=15 cent
10 cent
5 cent
0 cent
Mealy machine
Moore and Mealy machine state diagrams for the vending machine FSM
Reset / 0 ( N
( ND
Reset
Reset
Reset / 0
N / 0
D / 0
N / 0
N+D/
N+D
N
D
N
D
D/
N (^) D
N (^) D / 0
N (^) D
N (^) D / 0
Reset)/^
D Reset)/
Reset Reset / 1
13
00 01 11 10
00
01
11
10
Q 1
Q 0
DN
00 01 11 10
00
01
11
10
Q 1
Q 0
DN
00 01 11 10
00
01
11
10
Q 1
Q 0
DN
0 0 1 1
0 1 1 1
x x x x
1 1 1 1
0 1 1 0
1 0 1 1
x x x x
0 1 1 1
0 0 1 0
0 0 1 0
x x x x
0 0 1 0
K-map for D 1
K-map for D 0
K-map for Open (Moore)
D 1
= Q 1
·N
D N Q Q N Q N Q D 0 0 0 1 1
OPEN = Q 1
·Q 0
OPEN = Q1·Q 0
D·Q 0
D·Q 1
N·Q 1
Moore
Mealy
00 01 11 10
00
01
11
10
Q 1
Q 0
DN
0 0 1 0
0 0 1 1
x x x x
0 1 1 1
K-map for Open (Mealy)
14
D Q
R Q
D Q
R Q
Q 0
N
N
Q 0
Q 1
N
Q 1
D
D 0
D 1
Q 1
OPEN
D
0
Q
CLK
CLK
Vending machine FSM implementation based on D flip-flops(Moore).
0
Q
1
Q
Q 1
Q 0
Reset
Reset
16
00 01 11 10
00
01
11
10
Q 1
Q 0
DN
00 01 11 10
00
01
11
10
Q 1
Q 0
DN
00 01 11 10
00
01
11
10
Q 1
Q 0
DN
00 01 11 10
00
01
11
10
Q 1
Q 0
DN
0 0 x x
0 1 x x
x x x x
1 1 x x
x x 0 0
x x 0 0
x x x x
x x 0 0
0 x x 0
1 x x 1
x x x x
0 x x 1
x 0 0 x
x 1 0 x
x x x x
x 0 0 x
K-map for J (^1) K-map for K 1
K-map for J 0
K-map for K 0
K-maps for J-K flip-flop implementation of vending machine.
1
0
1
0 0 1
K Q N 0 1
17
J Q
R Q
Q 1
CLK
K
J Q
R Q
Q 0
CLK
K
OPEN N
Q 0
D
N
D
Q 1
N
0
Q
1
Q
0
Q
1
Q
J-K flip-flop implementation for the vending machine example (Moore).
Similarly, a Mealy implementation; only the OPEN function changes.
Reset
19
20
1 received 1 received 1 received
i=
i=
i=2 i=
[0]
i=
[0]
i=
[1]
Reset
Reset
0/
0/
0/
1/
1/
00
10
01 1
1
1
0
0
0
Mealy Machine Moore Machine
Input
Output
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