COMP541 State Machines

1. COMP541State Machines Montek Singh Feb 8, 2012

2. Today’s Topics • State Machines • How to design machines that go through a sequence of events • “sequential machines” • Basically close the feedback loop in this picture:

3. Synchronous Sequential Logic • Flip-flops/registers contain the system’s state • state changes only at clock edge • so system is synchronized to the clock • all flip-flops receive the same clock signal (important!) • every cyclic path must contain a flip-flop

4. Two common types • Two common synchronous sequential circuits: • Finite State Machines (FSMs) • Pipelines

5. Finite State Machine (FSM) • Consists of: • State register that • holds the current state • updates it to the “next state” at clock edge • Combinational logic (CL) that • computes the next state • using current state and inputs • computes the outputs • using current state (and maybe inputs)

6. More and Mealy FSMs • Two types of finite state machines differ in the output logic: • Moore FSM: • outputs depend only on the current state • Mealy FSM: • outputs depend on the current state and the inputs • can convert from one form to the other • Mealy is more general • In Both: • Next state is determined by current state and inputs

7. Moore and Mealy FSMs

8. FSM Example • Traffic light controller • Traffic sensors: TA, TB (TRUE when there’s traffic) • Lights: LA, LB

9. FSM Black Box • Inputs: • CLK, Reset, TA, TB • Outputs: LA, LB

10. Design Simple FSM • When reset, LA is green and LB is red • As long as traffic on Academic (TA high), keep LA green • When TA goes low, sequence to traffic on Bravado • Follow same algorithm for Bravado • Let’s say clock period is 5 sec (time for yellow light)

11. States • What sequence do the traffic lights follow? • Reset  State 0, LA is green and LB is red • Next (on board)?

12. State Transition Diagram • Moore FSM: outputs labeled in each state • States: Circles • Transitions: Arcs

13. State Transition Table

14. FSM Encoded State Transition Table

15. FSM Output Table

16. FSM Schematic: State Register

17. Next State Logic

18. Output Logic

19. FSM Timing Diagram: Study carefully!

20. Design Procedure • Take problem description and refine it into a state table or diagram • Assign codes to the states • Derive Boolean equations and implement • Or, write Verilog and compile

21. Example: Sequence Recognizer • Circuit has input, X, and output, Z • Recognizes sequence 1101 on X • Specifically, if X has been 110 and next bit is 1, make Z high

22. How to Design States • States remember past history • Clearly must remember we’ve seen 110 when next 1 comes along • Tell me one necessary state for this example…?

23. Beginning State • Start state: let’s call it A • if 1 appears on input, move to next state B • output remains at 0 Input / Output

24. Second 1 • New state, C • To reach C, must have seen 11

25. Next a 0 • If 110 has been received, go to D • Next 1 will generate a 1 on output Z

26. What else? • What happens to arrow on right? • Must go to some state. • Where?

27. What Sequence? • Here we have to interpret the problem statement • We’ve just seen 01 • Is this beginning of new 1101? • Or do we need to start over w/ another 1? • Textbook: decides that it’s beginning (01…)

28. Cover every possibility • Well, must have every possibility out of every state • In this case, just two: X = 0 or 1 • You fill in other cases

29. Fill in

30. Full Answer

31. State Minimization • When we make state diagram, do we need all those states? • Some may be redundant • State minimization procedures can be used • Is a tough problem (NP-complete) • but pretty good algorithms exist • exact and approximate • We won’t cover in this course

32. Reading • Read 3.4-3.6 • Might be good to look at Chapter 4 (Verilog only)