fsm word problems - university of california, san diego · fsm word problems . fsm example...
TRANSCRIPT
FSM Example
• Traffic light controller
– Traffic sensors: TA, TB (TRUE when there’s traffic)
– Lights: LA, LB
– If LA = GREEN, then LA remains GREEN as long as A has cars (i.e. TA = 1)
– If LB = GREEN, then LB remains GREEN as long as B has cars (i.e. TB = 1)
– Light colors change (GREEN, RED) → (YELLOW, RED) → (RED, GREEN)
Modified FSM Example
• If LA is GREEN: Case
– No cars on either A or B: change light after 16 cycles
– Cars waiting on both A and B: change light after 16 cycles
– Cars waiting only on A: LA stays GREEN
– Cars waiting only on B: change light
– Light colors change (GREEN, RED) → (YELLOW, RED) → (RED, GREEN)
• If LB is GREEN: Case …
FSM Blackbox
• FSM Inputs: CLK, TA, TB, CR (to reset counter)
• FSM Outputs: LA, LB, CT (TRUE if count is 15, all 1’s)
• Datapath: 4-bit counter
Traffic Light
Controller
TA
TB
LA
LB
CLK
Reset
+
2
2
4
MUX
4
4
“0001”
4 4
“0000”
0 1
CR
4
CT
CT CR
4-bit D-FFs
4-input AND
FSM State Transition Diagram
S0 LA = G LB= R CR= 1
S1 LA = G LB= R CR= 0
S2 LA = Y LB= R CR= *
S3 LA = R LB= G CR= 1
S4 LA = R LB= G CR= 0
S5 LA = R LB= Y CR= *
Reset
CT
CT
CT
CT
TA TB
TA TB
TA TB
TA TB
TA
TB TA
TB
TA TB
TB TA
LA LB LA LB LA LB
LA LB LA LB LA LB
String Recognition
• Simple case: recognize 1101
“ ” 0
“1” 0
“11” 0
Reset
1 “110”
0
1 0 1 “1101”
1
1
1
0 0
0
0
String Recognition
• General rules:
1. Create string matching tree
2. State output = 1 if a “pattern” is contained along the path
3. Add failure edges: find longest “suffix” of string seen so far and transition to the corresponding “prefix” state
String Recognition
• Example: 1101, 1011, 101
1. Create string matching tree
2. State output = 1 if a “pattern” is contained along the path
3. Add failure edges: find longest “suffix” of string seen so far and transition to the corresponding “prefix” state
“ ” 0
“1” 0
“11” 0
Reset
1 “110”
0
1 0 1 “1101”
1
“10” 0
0
“101” 1
“1011” 1
1 1
String Recognition
• Example: 1111, 1011, 101
1. Create string matching tree
2. State output = 1 if a “pattern” is contained along the path
3. Add failure edges: find longest “suffix” of string seen so far and transition to the corresponding “prefix” state
“ ” 0
“1” 0
“11” 0
Reset
1 “111”
0
1 1 1 “1111”
1
“10” 0
0
“101” 1
“1011” 1
0 0
0
1 0
1 1
0
0
1
0