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Lecture 10 Finite State Machine Design

Lecture 10 Finite State Machine Design. Hai Zhou ECE 303 Advanced Digital Design Spring 2002. 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.

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Lecture 10 Finite State Machine Design

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  1. Lecture 10Finite State Machine Design Hai Zhou ECE 303 Advanced Digital Design Spring 2002 ECE C03 Lecture 10

  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 ECE C03 Lecture 10

  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 Symbolic State Transition Table 1 Odd Present State Input Next State Output [1] 0 0 0 0 0 0 1 1 0 1 0 1 1 State Diagram 1 1 0 1 Encoded State Transition Table ECE C03 Lecture 10

  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 1 0 1 1 0 0 1 0 1 1 Output ECE C03 Lecture 10 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 ECE C03 Lecture 10

  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 ECE C03 Lecture 10

  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 S7 S8 [open] [open] ECE C03 Lecture 10

  8. Vending Machine Example Present Next Output State D N State Open 0¢ 0 0 0¢ 0 0 1 5¢ 0 1 0 10¢ 0 1 1 X X D 5¢ 0 0 5¢ 0 0 1 10¢ 0 1 0 15¢ 0 1 1 X X D 10¢ 0 0 10¢ 0 0 1 15¢ 0 1 0 15¢ 0 1 1 X X 15¢ X X 15¢ 1 Step 3: State Minimization Inputs Reset 0¢ N 5¢ N 10¢ N, D 15¢ [open] reuse states whenever possible Symbolic State Table ECE C03 Lecture 10

  9. Vending Machine Example Present State Next State Output Q Q D N D D Open 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 1 1 X X X 0 1 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 1 X X X 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 1 1 X X X 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 X X X Step 4: State Encoding Inputs ECE C03 Lecture 10

  10. Vending Machine Example Q 1 D Q 1 1 \ Q Q 1 0 \ Q 0 Q 0 \ N D Q 0 0 Q \ Q 1 0 Q 1 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 D1 K-map for D0 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 N 8 Gates R \reset ECE C03 Lecture 10 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 i Combinational 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 ECE C03 Lecture 10

  12. Equivalence of Moore and Mealy Machines N D D D N D 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¢ N D/0 D/0 [0] N N/0 10¢ 10¢ D/1 [0] N D/0 N+D N+D/1 15¢ 15¢ [1] Reset Reset/1 Outputs are associated with State Outputs are associated with Transitions ECE C03 Lecture 10

  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] ECE C03 Lecture 10

  14. Analyze Behavior of Moore Machines Reverse engineer the following: X J A Q Input X Output Z State A, B = Z C X \A K Q \B R FFa \Reset Clk X J Z Q C X \B K Q \A R FFb \Reset Two Techniques for Reverse Engineering: • Ad Hoc: Try input combinations to derive transition table • Formal: Derive transition by analyzing the circuit ECE C03 Lecture 10

  15. Ad Hoc Reverse Engineering Reset X = 1 X = 0 X = 1 X = 0 X = 1 X = 0 X = 0 AB = 00 AB = 00 AB = 1 1 AB = 1 1 AB = 10 AB = 10 AB = 01 AB = 00 Behavior in response to input sequence 1 0 1 0 1 0: 100 X Clk A Z \Reset Partially Derived State Transition Table ECE C03 Lecture 10

  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 -> State 00 State 01, Input 1 -> State 01 B+ ECE C03 Lecture 10

  17. Behavior of Mealy Machines \ A \ A \ B \ X \ X \ X 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 ECE C03 Lecture 10

  18. Ad Hoc Reverse Engineering Reset X =1 X =0 X =1 X =0 X =1 X =1 AB =00 AB =00 AB =00 AB =01 AB =1 1 AB =10 AB =01 Z =0 Z =0 Z =0 Z =0 Z =1 Z =1 Z =0 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 ECE C03 Lecture 10

  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 -> State 01, Output 1 State 10, Input 0 -> State 00, Output 0 State 11, Input 1 -> State 11, Output 1 A+ B+ Z ECE C03 Lecture 10

  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 ECE C03 Lecture 10

  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… ECE C03 Lecture 10

  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] ECE C03 Lecture 10

  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] ECE C03 Lecture 10

  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] ECE C03 Lecture 10

  25. Finite String Recognizer Reset S0 [0] S4 S1 [0] [0] S2 S5 [0] [0] S3 S6 [1] [0] 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 ECE C03 Lecture 10

  26. Review of Design Process • Write down sample inputs and outputs to understand specification • Write down sequences of states and transitions for the sequences to be recognized • Add missing transitions; reuse states as much as possible • Verify I/O behavior of your state diagram to insure it functions like the specification ECE C03 Lecture 10

  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 to Yellow to Red, allowing highway to return to 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. ECE C03 Lecture 10

  28. Traffic Light Controller Picture of Highway/Farmroad Intersection: Farmroad C HL FL Highway Highway FL HL C Farmroad ECE C03 Lecture 10

  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 assert 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 yellow (farmroad red) Farmroad green (highway red) Farmroad yellow (highway red) State S0 S1 S2 S3 ECE C03 Lecture 10

  30. Traffic Light Controller Compare with state diagram: TL + C Reset S0: HG S1: HY S2: FG S3: FY S0 TL•C/ST TS/ST TS S1 S3 TS TS/ST TL + C/ST S2 TL • C Advantages of State Charts: • Concentrates 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 ECE C03 Lecture 10

  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 ECE C03 Lecture 10

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