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## Lecture 10 Finite State Machine Design

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### Title: Lecture 8 Memory Elements and Clocking Author: Preferred Customer Last modified by: haizhou Created Date: 6/17/1995 11:31:02 PM Document presentation format – PowerPoint PPT presentation

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Title: Lecture 10 Finite State Machine Design

1
Lecture 10Finite State Machine Design
• Hai Zhou
• ECE 303
• Spring 2002

2
Outline
• Review of sequential machine design
• Moore/Mealy Machines
• FSM Word Problems
• Finite string recognizer
• Traffic light controller
• READING Katz 8.1, 8.2, 8.4, 8.5, Dewey 9.1, 9.2

3
Example Odd Parity Checker
Assert output whenever input bit stream has odd
of 1's
Reset
Present State
Input
Next State
Output
Even
0
Even
0
Even
1
Odd
0
0
Even
Odd
0
Odd
1
0
Odd
1
Even
1
1
1
Symbolic State Transition Table
Odd
Output
Next State
Input
Present State
1
0
0
0
0
0
0
1
1
0
1
1
0
1
State Diagram
1
0
1
1
Encoded State Transition Table
4
Odd Parity Checker Design
Next State/Output Functions
NS PS xor PI OUT PS
Input
Output
T
Q
NS
Input
CLK
D
Q
PS/Output
Q
CLK
R
Q
R
\Reset
\Reset
T FF Implementation
D FF Implementation
Input
1
0
0
1
1
0
1
0
1
1
1
0
Clk
1
1
0
1
0
0
1
1
0
1
1
1
Output
Timing Behavior Input 1 0 0 1 1 0 1 0 1 1 1 0
5
Basic Design Approach
1. Understand the statement of the
Specification 2. Obtain an abstract
specification of the FSM 3. Perform a state
mininimization 4. Perform state
assignment 5. Choose FF types to implement FSM
state register 6. Implement the FSM
1, 2 covered now 3, 4, 5 covered later 4, 5
generalized from the counter design procedure
6
Example Vending Machine FSM
General Machine Concept
deliver package of gum after 15 cents
deposited single coin slot for dimes,
nickels no change
Step 1. Understand the problem
Draw a picture!
N
Block Diagram
Coin
Vending
Gum
Open
D
Sensor
Machine
Release
FSM
Mechanism
Reset
Clk
7
Vending Machine Example
Step 2. Map into more suitable abstract
representation
Reset
S0
Tabulate typical input sequences
N
D
three nickels nickel, dime dime, nickel two
dimes two nickels, dime
S1
S2
D
N
D
N
Draw state diagram
S4
S6
S3
S5
Inputs N, D, reset Output open
open
open
open
N
D
S8
S7
open
open
8
Vending Machine Example
Step 3 State Minimization
Inputs
Reset
0
N
5
N
10
N, D
15
open
reuse states whenever possible
Symbolic State Table
9
Vending Machine Example
Step 4 State Encoding
Inputs
10
Vending Machine Example
Step 5. Choose FFs for implementation
D FF easiest to use
Q1
Q1
Q1
Q1 Q0
Q1 Q0
Q1 Q0
D N
D N
D N
0 1 1 0
0 0 1 1
0 0 1 0
1 0 1 1
0 0 1 0
0 1 1 1
N
N
N
X X X X
X X X X
X X X X
D
D
D
1 1 1 1
0 1 1 1
0 0 1 0
Q0
Q0
Q0
K-map for D0
K-map for D1
K-map for Open
D
D
Q
D1 Q1 D Q0 N D0 N Q0 Q0 N Q1 N
Q1 D OPEN Q1 Q0
CLK
Q
R
N
\reset
N
OPEN
D
Q
CLK
Q
8 Gates
N
R
\reset
D
11
Moore and Mealy Machine Design Procedure
Moore Machine Outputs are function solely of the
current state Outputs change synchronously
with state changes
State
Register
Comb.
X
Combinational
i
Logic for
Inputs
Logic for
Outputs
Next State
Z
(Flip-flop
k
Outputs
Inputs)
Clock
state
feedback
Mealy Machine Outputs depend on state AND
inputs Input change causes an immediate
output change Asynchronous signals
Z
X
k
i
Combinational
Outputs
Inputs
Logic for
Outputs and
Next State
State
Feedback
State Register
Clock
12
Equivalence of Moore and Mealy Machines
Moore Machine
N D Reset
Mealy Machine
(N D Reset)/0
Reset/0
Reset
0
0
0
Reset
Reset/0
N
N/0
5
5
D/0
N D/0
0
N
N/0
10
10
D/1
0
N D/0
ND
ND/1
15
15
1
Reset
Reset/1
Outputs are associated with State
Outputs are associated with Transitions
13
States vs Transitions
Mealy Machine typically has fewer states than
Moore Machine for same output sequence
0
0/0
0
0
0
Same I/O behavior Different of states
1/0
0/0
0
1
0
1
1
1/1
0
1
2
1
1
14
Analyze Behavior of Moore Machines
Reverse engineer the following
J
X
A
Q
Input X Output Z State A, B Z
C
X
\A
K
Q
R
\B
FFa
\Reset
Clk
J
X
Z
Q
C
X
\B
K
Q
R
\A
FFb
\Reset
Two Techniques for Reverse Engineering Ad
Hoc Try input combinations to derive transition
table Formal Derive transition by
analyzing the circuit
15
Behavior in response to input sequence 1 0 1 0 1
0
100
X
Clk
A
Z
\Reset
Partially Derived State Transition Table
16
Formal Reverse Engineering
Derive transition table from next state and
output combinational functions presented to
the flipflops!
Z B
Ka X B Kb X xor A
Ja X Jb X
FF excitation equations for J-K flipflop
A Ja A Ka A X A (X B)
A B Jb B Kb B X B (X A
X A) B
Next State K-Maps
A
State 00, Input 0 -gt State 00 State 01, Input 1
-gt State 01
B
17
Behavior of Mealy Machines
Clk
X
A
B
D
Q
J
Q
DA
C
C
Q
K
Q
R
R
\Reset
\Reset
A
DA
X
B
B
Z
X
A
Input X, Output Z, State A, B
State register consists of D FF and J-K FF
18
Signal Trace of Input Sequence 101011
100
Note glitches in Z! Outputs valid at following
falling clock edge
X
Clk
A
B
Z
\Reset
Partially completed state transition table based
on the signal trace
19
Formal Reverse Engineering
A B (A X) A B B X B Jb
B Kb B (A xor X) B X B
A B  X A B X B X Z A X
B X
Missing Transitions and Outputs
State 01, Input 0 -gt State 01, Output 1 State 10,
Input 0 -gt State 00, Output 0 State 11, Input 1
-gt State 11, Output 1
A
B
Z
20
Finite State Machine Word Problems
Mapping English Language Description to Formal
Specifications
Case Studies Finite String Pattern
Recognizer Traffic Light Controller
We will use state diagrams and ASM Charts
21
Finite String Pattern Recognizer
A finite string recognizer has one input (X) and
one output (Z). The output is asserted whenever
the input sequence 010 has been observed, as
long as the sequence 100 has never
been seen. Step 1. Understanding the problem
statement Sample input/output
behavior
X 00101010010 Z 00010101000 X
11011010010 Z 00000001000
22
Finite String Recognizer
Step 2. Draw State Diagrams/ASM Charts for the
strings that must be recognized.
I.e., 010 and 100.
Reset
S0
0
Moore State Diagram Reset signal places FSM in
S0
S4
S1
0
0
S2
S5
0
0
S3
S6
Loops in State
Outputs 1
1
0
23
Finite String Recognizer
Exit conditions from state S3 have recognized
010 if next input is 0 then have 0100!
if next input is 1 then have 0101 01
(state S2)
Reset
S0
0
S4
S1
0
0
S2
S5
0
0
S3
S6
1
0
24
Finite String Recognizer
Exit conditions from S1 recognizes strings of
form 0 (no 1 seen) loop back to S1 if
input is 0 Exit conditions from S4 recognizes
strings of form 1 (no 0 seen) loop back to
S4 if input is 1
Reset
S0
0
S4
S1
0
0
S2
S5
0
0
S3
S6
1
0
25
Finite String Recognizer
S2, S5 with incomplete transitions S2 01 If
next input is 1, then string could be prefix of
(01)1(00) S4 handles just this
case! S5 10 If next input is 1, then string
could be prefix of (10)1(0) S2
handles just this case!
Final State Diagram
26
Review of Design Process
Write down sample inputs and outputs to
understand specification Write down
sequences of states and transitions for the
missing transitions reuse states as much as
possible Verify I/O behavior of your state
diagram to insure it functions like the
specification
27
Traffic Light Controller
A busy highway is intersected by a little used
farmroad. Detectors C sense the presence of cars
waiting on the farmroad. With no car on
farmroad, light remain green in highway
direction. If vehicle on farmroad, highway
lights go from Green to Yellow to Red, allowing
the farmroad lights to become green. These stay
green only as long as a farmroad car is detected
but never longer than a set interval. When
these are met, farm lights transition from Green
green. Even if farmroad vehicles are waiting,
highway gets at least a set interval as
green. Assume you have an interval timer that
generates a short time pulse (TS) and a long time
pulse (TL) in response to a set (ST) signal.
TS is to be used for timing yellow lights and TL
for green lights.
28
Traffic Light Controller
C
HL
FL
Highway
Highway
FL
HL
C
29
Traffic Light Controller
Tabulation of Inputs and Outputs
Input Signal reset C TS TL Output Signal HG, HY,
HR FG, FY, FR ST
Description place FSM in initial state detect
vehicle on farmroad short time interval
expired long time interval expired Description as
sert green/yellow/red highway lights assert
green/yellow/red farmroad lights start timing a
short or long interval
Tabulation of Unique States Some light
configuration imply others
Description Highway green (farmroad red) Highway
State S0 S1 S2 S3
30
Traffic Light Controller
Compare with state diagram
TL C
Reset
S0 HG S1 HY S2 FG S3 FY
S0
TLC/ST
TS/ST
TS
S1
S3
TS
TS/ST
TL C/ST
S2
TL C
on paths and conditions for exiting a state
Exit conditions built up incrementally, later
combined into single Boolean
condition for exit Easier to understand
the design as an algorithm
31
Summary
• Review of sequential machine design
• Moore/Mealy Machines
• FSM Word Problems
• Finite string recognizer
• Traffic light controller
• NEXT LECTURE Finite State Machine Optimization
• READING Katz 9.1, 2.2.1, 9.2.2, Dewey 9.3