# Basic Finite State Machines 1. 2 Finite State Machines Binary encoded state machines –The number of flip-flops is the smallest number m such that 2 m.

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Basic Finite State Machines 1

2 Finite State Machines Binary encoded state machines –The number of flip-flops is the smallest number m such that 2 m n, where n is the number of states in the machine. –Next state logic equations are dependent on all of the flip-flops in the implementation. Natural for CPLDs, where CPLDs have high fan-in logic gates. –There may be unused states.

Basic Finite State Machines 3 Finite State Machines Gray encoded state machines –Similar to binary encoded state machines. –State sequence has the property that only one output changes when sequencing between states. –Can have lower power –Can be asynchronously sampled in some systems. –There may be unused states.

Basic Finite State Machines 4 Finite State Machines One-Hot Finite State Machines –One flip-flop for each state in the machine –Normal operation has exactly one flip-flop set; all other flip-flops reset. –Next state logic equations for each flip-flop depend solely on a single state (flip-flop) and external inputs. –Natural for FPGAs, which dont have high fan- in logic gates and an abundance of flip-flops.] –There will be unused states

Basic Finite State Machines 5 Finite State Machines Modified One-Hot Finite State Machines –n-1 flip-flops for an n-state machine –Normal operation has zero or one flip-flop set The all zeros state is a legitimate state –There will be unused states

Basic Finite State Machines 6 Finite State Machines Linear Feedback Shift Register (LFSR) –The number of flip-flops is the smallest number m such that 2 m n, where n is the number of states in the machine. –Shift register with XOR feedback –Maximal length shift registers can have 2 m -1 states. –Can modify the circuit to support 2 m states.

Basic Finite State Machines 7 Finite State Machines Example Linear Feedback Shift Register Two or four taps

Basic Finite State Machines 8 Finite State Machines Johnson Ring Counter –Also called twisted-ring or Mobius counter –For n flip-flops, it will have 2n states. –Shift register with inverted feedback –Unmodified, it will have unused states –Can modify the circuit to support 2n-1 states.

Basic Finite State Machines 9 Encoding Efficiency: Binary vs. One Hot

Basic Finite State Machines 10 Finite State Machines CAE Tools - Synthesizers –Generates logic to implement a function, guided by the user. –Typically does not generate logic for either fault detection or correction, important for military and aerospace applications.

Basic Finite State Machines 11 Finite State Machines Lockup State –A state or sequence of states outside the normal flow of the FSM that do not lead back to a legal state.

Basic Finite State Machines 12 Lockup States Sample State Machine Home Ping One Two Three Reset

Basic Finite State Machines 13 Library IEEE; Use IEEE.Std_Logic_1164.All; Entity Onehot_Simple_Act Is Port ( Clk : In Std_Logic; Reset : In Std_Logic; Ping : Out Std_Logic ); End Onehot_Simple_Act; Library IEEE; Use IEEE.Std_Logic_1164.All; Architecture Onehot_Simple_Act of Onehot_Simple_Act Is Type StateType Is ( Home, One, Two, Three ); Signal State : Statetype; Begin M: Process ( Clk, Reset ) Begin If ( Reset = '1' ) Then State <= Home; Else If Rising_Edge (Clk) Then Case State Is When Home => State <= One; When One => State <= Two; When Two => State <= Three; When Three => State <= Home; End Case; End If; End Process M; O: Process (State) Begin If (State = Home) Then Ping <= '1'; Else Ping <= '0'; End If; End Process O; End Onehot_Simple_Act; Enumeration Next-state Logic All states covered

Basic Finite State Machines 14 Lockup States A Synthesized One-Hot Implementation Typical ring counter with lockup states was synthesized.

Basic Finite State Machines 15 Lockup States Another Synthesized One-Hot Implementation Note: Results depend on version of synthesis software. This circuit was synthesized with the same product used in the previous slide. Note this is a modified one-hot FSM.

Basic Finite State Machines 16 Modified one-hot state machine (reset logic omitted) for a 4-state, two- phase, non-overlapping clock generator. A NOR of all flip-flop outputs and the home state being encoded as the zero vector adds robustness. Standard one-hot state machines [Q3 would be tied to the input of the first flip] have 1 flip-flop per state, with exactly one flip-flop set per state, presenting a non-recoverable SEU hazard. Lockup States Yet Another Synthesized One-Hot Implementation (free product)

Basic Finite State Machines 17 Lockup States A Safe One-Hot Implementation (Synthesized) Reset flip-flops. Note second one is on falling edge of the clock. This implementation uses 6 flip-flops.

Basic Finite State Machines 18 Lockup States A Safe One-Hot Implementation (Synthesized) Reset flip-flops. Note second one is on falling edge of the clock. This implementation uses 6 flip-flops.

Basic Finite State Machines 19 Lockup States - Binary Encoding Home Ping One Two Three Four Three unused states. (Five, Six, Seven)

Basic Finite State Machines 20 Lockup States Binary Encoding Type StateType Is ( Home, One, Two, Three, Four); Signal State : Statetype; … Case State Is … When Others => State <= Home; When Others refers to the logical states in the VHDL enumeration, not the physical implementation. Also, states that are not reachable can be deleted, depending on the software and settings.

Basic Finite State Machines 21 Two Most Common Finite State Machine (FSM) Types Binary: Smallest m (flip-flop count) with 2m n (state count), highest encoding efficiency. –Or Gray Coded, a re-mapping of a binary FSM One Hot: m = n, i.e., one flip-flop per state, lowest encoding efficiency. –Or Modified One Hot: m = n-1 (one state represented by 0 vector).

Basic Finite State Machines 22 Issue: How To Protect FSMs Against Transient Errors (SEUs and MEUs): Illegal State Detection Adding Error Detection and Correction (EDAC) Circuitry

Basic Finite State Machines 23 Binary and Gray Codes FSM State Sequences 0 0 0 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 0 3-bit Reflected Gray Code 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 Binary Code Binary sequence can have 0 (hold), 1, 2,..., n bits changing from state to state. Gray code structure ensures that either 0 (hold) or 1 bit changes from state to state. Illegal states in either type are detected in the same way, i.e., by explicit decoding.

Basic Finite State Machines 24 Gray Code Illegal Transition Detection Next State Logic State Bit Register Last State Register >1 logic 1 Bit-wise XOR inputs outputs illegal transition False illegal transition indications can also be triggered by errors in the Last State Register, and doubling the number of bits doubles the probability of an SEU.

Basic Finite State Machines 25 One Hot FSM Coding Many (2 n -n) unused states - not "reachable" from VHDL 2. Illegal state detection circuitry complex Parity (odd) will detect all SEUs, not MEUs 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 Binary Code One Hot Coding 2 "The Impact of Software and CAE Tools on SEU in Field Programmable Gate Arrays," R. Katz, et. al., IEEE Transactions on Nuclear Science, December, 1999.

Basic Finite State Machines 26 One Hot FSM Coding Example of Lockup 7 6 5 4 3 2 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 One Hot FSM without protection. SEU FSM is locked up.

Basic Finite State Machines 27 Modified One Hot FSM Coding 7 6 5 4 3 2 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 One Hot Coding 6 5 4 3 2 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 Modified One Hot Coding Note: Sometimes used by synthesis when one hot FSM specified. Modified one hot codings use one less flip-flop.

Basic Finite State Machines 28 Modified One Hot FSM Illegal State Detection Error detection more difficult than for one hot –1 0 upsets result in a legal state. –Parity will not detect all SEUs. –If an SEU occurs, most likely the upset will be detectable Recovery from lockup sequence simple If all 0's (NOR of state bits), then generate a 1 to first stage. –If multiple 1's (more difficult to detect), then will wait until all 1's are "shifted out."

Basic Finite State Machines 29 Discuss Hamming Codes (to be included)

Basic Finite State Machines 30 Is There a Best FSM Type, and Is It Best Protected Against Transient Errors By Circuit-Level or System-Level EDAC? Circuit-level EDAC –Expensive in power and mass if used to protect all circuits –Can be defeated by multiple-bit transient errors –Can be defeated by clock upset System-level EDAC –Required for hard-failure handling –Relies on inherent redundancy in system, high-level error checking, and some EDAC hardware

Basic Finite State Machines 31 But It Gets Worse … Some synthesizers may replicate flip-flops. Block A Block B Block C Block D Block B Block C Block D Block A

Basic Finite State Machines 32 And Worse... Backend software may also replicate flip- flops This can be bad if the flip-flop is used to synchronize an asynchronous signal.

Basic Finite State Machines 33 And Yet Worse... Logic Translation/Optimization Original Optimized Yes, the designer used this point to synchronize signals and drive a motor. The short circuit was bad.

Basic Finite State Machines 34 What Can You Do? Some Helpful Hints and Points for Discussion CONTROL Your Design –Schematic vs. HDL –Constant encodings vs. enumeration Manual State Assignment –Dont leave unused states - add Dummy States Add logic to trick the synthesizer to think they are used as otherwise they may be optimized out. This may include adding a test signal to sequence through unused states as well as bringing out dummy outputs.

Basic Finite State Machines 35 What Can You Do? More Helpful Hints and Points for Discussion Ban All FPGAs

Basic Finite State Machines 36 What Can You Do? More Helpful Hints and Points for Discussion Monitor Your Design –Check The Synthesizer Listings Number of flip-flops –Too many flip-flops; replication? –Too few flip-flops; eliminated your TMR or parity? Reports of replication Is the state assignment one that you asked for? Sometimes the synthesizer thinks it knows best.

Basic Finite State Machines 37 What Can You Do? More Helpful Hints and Points for Discussion Monitor Your Design (continued) –Check Flip-Flop Reports Has it moved flip-flops into the I/O cells with perhaps poor SEU performance? Substituted an S-Module based flip-flop for your C- Module based one? Did the synthesizer generate TMR the way you asked for it or just ignore you?

Basic Finite State Machines 38 What Can You Do? More Helpful Hints and Points for Discussion Monitor Your Design (continued) –Check Auxiliary Files Check list of cells that the optimizer deleted –Generate Schematics for Critical Areas of Synthesized Logic This may uncover some rather interesting surprises. Send them to me for the next seminar; win a free Diet Coke.

Basic Finite State Machines 39 What Can You Do? More Helpful Hints and Points for Discussion Verify your design thoroughly –Do not rely solely on simulation!!!!! Look and think. Do not rely on these tools to do your thinking for you.

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