1. CSE 370 – Winter 2002 - Sequential Logic-2 - 1
Overview
Last lecture
“Complex” counters
Finite state machines
Example: Parity checker
Today
Example: Ant in a maze
More on Moore vs. Mealy
2/28/2019
CSE 370 – Winter Sequential Logic-2 - 1

2. Example: ant brain (Ward, MIT)
Sensors: L and R antennae, 1 if in touching wall
Actuators: F - forward step, TL/TR - turn left/right slightly
Goal: find way out of maze
Strategy: keep the wall on the right
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CSE 370 – Winter Sequential Logic-2 - 2

3. CSE 370 – Winter 2002 - Sequential Logic-2 - 3
Ant behavior
A: Following wall, touching Go forward, turning left slightly
B: Following wall, not touching Go forward, turning right slightly
D: Hit wall again Back to state A
C: Break in wall Go forward, turning right slightly
E: Wall in front Turn left until...
F: ...we are here, same as state B
G: Turn left until...
LOST: Forward until we touch something
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CSE 370 – Winter Sequential Logic-2 - 3

4. CSE 370 – Winter 2002 - Sequential Logic-2 - 4
Designing an ant brain
State diagram
L + R
L’ R
LOST
(F)
L’ R’
E/G (TL)
L + R R A
(TL, F) L
L’ R’ B
(TR, F)
L’ R’ R
C (TR, F) R’ R’
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CSE 370 – Winter Sequential Logic-2 - 4

5. Synthesizing the ant brain circuit
Encode states using a set of state variables
arbitrary choice - may affect cost, speed
Use transition truth table
define next state function for each state variable
define output function for each output
Implement next state and output functions using combinational logic
2-level logic (ROM/PLA/PAL)
multi-level logic
next state and output functions can be optimized together
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CSE 370 – Winter Sequential Logic-2 - 5

6. Transition truth table
Using symbolic states and outputs
LOST
(F)
E/G (TL) A
(TL, F) B
(TR, F)
C (TR, F) R’
L’ R’ R L
L’ R
L + R
state L R next state outputs
LOST 0 0 LOST F
LOST – 1 E/G F
LOST 1 – E/G F
A 0 0 B TL, F
A 0 1 A TL, F
A 1 – E/G TL, F
B – 0 C TR, F
B – 1 A TR, F
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CSE 370 – Winter Sequential Logic-2 - 6

7. CSE 370 – Winter 2002 - Sequential Logic-2 - 7
Synthesis
5 states : at least 3 state variables required (X, Y, Z)
state assignment (in this case, arbitrarily chosen)
LOST - 000
E/G - 001
A - 010
B - 011
C - 100
state L R next state outputs
X,Y,Z X', Y', Z' F TR TL
it now remains to synthesize these 6 functions
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CSE 370 – Winter Sequential Logic-2 - 7

8. Synthesis of next state and output functions
state inputs next state outputs
X,Y,Z L R X+,Y+,Z+ F TR TL
e.g.
TR = X + Y Z
X+ = X R’ + Y Z R’ = R’ TR
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CSE 370 – Winter Sequential Logic-2 - 8

9. Circuit implementation
Outputs are a function of the current state only - Moore machine L R F TR TL
Next State
Current State
output logic
next state logic X+ Y+ Z+ X Y Z
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CSE 370 – Winter Sequential Logic-2 - 9

10. Don’t cares in FSM synthesis
What happens to the "unused" states (101, 110, 111)?
They were exploited as don't cares to minimize the logic
if the states can't happen, then we don't care what the functions do
if states do happen, we may be in trouble
000
(F)
001 (TL)
010
(TL, F)
011
(TR, F)
100 (TR, F) R’
L’ R’ R L
L’ R
L + R
111
101
110
Ant is in deep trouble
if it gets in this state
2/28/2019
CSE 370 – Winter Sequential Logic

11. CSE 370 – Winter 2002 - Sequential Logic-2 - 11
State minimization
Fewer states may mean fewer state variables
High-level synthesis may generate many redundant states
Two states are equivalent if they are impossible to distinguish from the outputs of the FSM, i. e., for any input sequence the outputs are the same
Two conditions for two states to be equivalent:
1) output must be the same in both states
2) must transition to equivalent states for all input combinations
2/28/2019
CSE 370 – Winter Sequential Logic

12. CSE 370 – Winter 2002 - Sequential Logic-2 - 12
Ant brain revisited
Any equivalent states?
LOST
(F)
E/G (TL) A
(TL, F) B
(TR, F)
C (TR, F) R’
L’ R’ R L
L’ R
L + R
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CSE 370 – Winter Sequential Logic

13. CSE 370 – Winter 2002 - Sequential Logic-2 - 13
New improved brain
Merge equivalent B and C states
Behavior is exactly the same as the 5-state brain
We now need only 2 state variables rather than 3
LOST
(F)
E/G (TL) A
(TL, F)
B/C
(TF, F) R’
L’ R’ R L
L’ R
L + R
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CSE 370 – Winter Sequential Logic

14. New brain implementation
state inputs next state outputs
X,Y L R X',Y' F TR TL X X+ Y R L X Y+ Y R L X F Y R L X TR Y R L X TL Y R L
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CSE 370 – Winter Sequential Logic

15. Mealy vs. Moore machines
Moore: outputs depend on current state only
Mealy: outputs may depend on current state and current inputs
Our ant brain is a Moore machine
output does not react immediately to input change
We could have specified a Mealy FSM
outputs have immediate reaction to inputs
as inputs change, so does next state, doesn’t commit until clocking event A
L’ R’ / TR, F
L / TL
L’ R / TL, F
react right away to leaving the wall
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CSE 370 – Winter Sequential Logic

16. Specifying outputs for a Moore machine
Output is a function of state only
Specify output in the state-diagram state bubble
Example: Detector for 01 or 10
current next reset input state state output
1 – – A 0
0 0 A B 0
0 1 A C 0
0 0 B B 0
0 1 B D 1
0 0 C E 1
0 1 C C 0
0 0 D E 1
0 1 D C 0
0 0 E B 0
0 1 E D 1
D/1
E/1
B/0
A/0
C/0 1
reset
2/28/2019
CSE 370 – Winter Sequential Logic

17. Specifying outputs for a Mealy machine
Output is a function of state and of inputs
Specify outputs on transition arcs
Example: Detector for 01 or 10 B A C
0/1
0/0
1/1
1/0
reset/0
current next reset input state state output
1 – – A 0
0 0 A B 0
0 1 A C 0
0 0 B B 0
0 1 B C 1
0 0 C B 1
0 1 C C 0
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CSE 370 – Winter Sequential Logic

18. Comparing Moore and Mealy machines
Mealy machines usually have less states
React faster to inputs – don't need to wait for clock
Asynchronous outputs and asynchronous feedback are dangerous
Moore machines are safer to use
Outputs change at clock edge (always one cycle later)
May need more logic to decode state into outputs
2/28/2019
CSE 370 – Winter Sequential Logic

19. CSE 370 – Winter 2002 - Sequential Logic-2 - 19
FSM design procedure
FSM-design procedure
1. State diagram and state-transition table
2. State minimization
3. State assignment (or state encoding)
4. Next-state logic minimization
5. Implement the design
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CSE 370 – Winter Sequential Logic

20. Example: vending machine
Release item after 15 cents are deposited
Single coin slot for dimes, nickels
No change
Reset N
Vending Machine FSM
Open
Coin Sensor
Release Mechanism D
Clock
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CSE 370 – Winter Sequential Logic

21. Example: vending machine (cont’d)
Suitable abstract representation
tabulate typical input sequences:
3 nickels
nickel, dime
dime, nickel
two dimes
draw state diagram:
inputs: N, D, reset
output: open chute
assumptions:
assume N and D asserted for one cycle
each state has a self loop for N = D = 0 (no coin) S0
Reset S1 N S2 D S3 N S4
[open] D S5
[open] N S6
[open] D S7
[open] N
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CSE 370 – Winter Sequential Logic

22. Example: vending machine (cont’d)
Minimize number of states - reuse states whenever possible 0¢
Reset
symbolic state table
present inputs next output state D N state open 0¢ ¢ ¢ ¢ – – 5¢ ¢ ¢ ¢ – – 10¢ ¢ ¢ ¢ – – 15¢ – – 15¢ 1
10¢ D 5¢ N
15¢
[open] D N
N + D
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CSE 370 – Winter Sequential Logic

23. Example: vending machine (cont’d)
Uniquely encode states
present state inputs next state output Q1 Q0 D N D1 D0 open – – – – – – – – – – –
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CSE 370 – Winter Sequential Logic

24. Example: vending machine (cont’d)
Mapping to logic
X X X X Q1 D1 Q0 N D D0
Open
D1 = Q1 + D + Q0 N
D0 = Q0’ N + Q0 N’ + Q1 N + Q1 D
OPEN = Q1 Q0
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CSE 370 – Winter Sequential Logic

25. Equivalent Mealy and Moore state diagrams
Moore machine
outputs associated with state
Mealy machine
outputs associated with transitions 0¢
[0]
10¢ 5¢
15¢
[1]
N’ D’ + Reset D N
N+D
N’ D’
Reset’
Reset 0¢
10¢ 5¢
15¢
(N’ D’ + Reset)/0
D/0
D/1
N/0
N+D/1
N’ D’/0
Reset’/1
Reset/0
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CSE 370 – Winter Sequential Logic

26. Example: vending machine (cont’d)
One-hot encoding (selecting state through a bit-vector process)
present state inputs next state output Q3 Q2 Q1 Q0 D N D3 D2 D1 D0 open
D0 = Q0 D’ N’
D1 = Q0 N + Q1 D’ N’
D2 = Q0 D + Q1 N + Q2 D’ N’
D3 = Q1 D + Q2 D + Q2 N + Q3
OPEN = Q3
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CSE 370 – Winter Sequential Logic