10/21/2016. A Finite State Machine (FSM) Models a System. ECE 120: Introduction to Computing. An FSM Consists of Five Parts
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1 University of Illinois at Urbana-Champaign Dept. of Electrical and Computer Engineering ECE 120: Introduction to Computing Finite State Machines (FSMs) A Finite State Machine (FSM) Models a System A model of a system system moves among a finite set of s motion based on external inputs produces external outputs Examples include: coin/bill-operated machines, many vehicle control systems, and computers executing programs. ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 1 ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 2 An FSM Consists of Five Parts 1. a finite set of s (bits) 2. a set of possible inputs (bits) 3. a set of possible outputs (bits) 4. a set of transition rules (Boolean expressions) 5. methods for calculating outputs (Bool. expr s) When implemented as a digital system, all parts of an FSM must be mapped to bits! A Digital FSM Must be Complete We implement FSMs as clocked synchronous sequential circuits. (So ID bits are stored in flip-flops.) Given any and any combination of inputs, a transition rule from the given to a next must be defined. Self-loops transitions from a to itself are acceptable. ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 3 ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 4
2 Use Keyless Entry as a Motivating Example A List of Abstract States Need Only List States meaning vehicle locked driver door unlocked all doors unlocked alarm sounding driver s door other doors Table is a list of abstract s. alarm on? LOCKED locked locked no DRIVER unlocked locked no UNLOCKED unlocked unlocked no ALARM locked locked yes In a list of abstract s, we can just list the s. Adding human meanings is optional (good to have if names are generic). Including outputs is also optional, and implies that outputs depend only on.* *An extra assumption that we will always make in our class. ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 5 ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 6 An Abstract Next-State Table Captures Expected Behavior To specify transitions, we use a next- table, which maps combinations of s and inputs into next s. This is an abstract next- table. action/input next LOCKED push unlock DRIVER DRIVER push unlock UNLOCKED (any) push lock LOCKED (any) push panic ALARM Abstract Next-State Table Does Not Answer All Questions We wrote transitions for typical use cases, but the table can be incomplete, ambiguous, and even inconsistent. For example, what happens if the user pushes lock and unlock at the same time? action/input next LOCKED push unlock DRIVER DRIVER push unlock UNLOCKED (any) push lock LOCKED (any) push panic ALARM ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 7 ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 8
3 Many Design Decisions are Usually Needed All such design decision questions should eventually be considered, and preferably answered. Be aware: any digital logic implementation will define answers. Only when any possible answer is acceptable should you make use of don t cares. Typically, you should review the final implementation to determine how any questions left open are answered. Abstract State Transition Diagram: the Same Information push lock We can represent the same information as a graph called an abstract transition diagram. push panic push unlock LOCKED DRIVER push lock push panic ALARM push lock push lock push panic push panic push unlock UN- LOCKED ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 9 ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 10 It s Time to Make Our Design Complete and Concrete The abstract next- table and the abstract transition diagram (can) contain exactly the same information. They answer the same questions. And neither is complete. So. It s time for bits! Let s Start with the State Identifiers How many bits do we need to identify a? There are 4 s.. Call them. S is for S(tate). ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 11 ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 12
4 All Outputs and Inputs Must Also Use Bits What about outputs? D driver door; 1 means unlocked R remaining doors; 1 means unlocked A alarm; 1 means alarm is sounding And inputs? U unlock button; 1 means it s been pressed L lock button; 1 means it s been pressed P panic button; 1 means it s been pressed We Next Choose a Representation for States Now we can choose a representation for s and rewrite our list of s. The order of s in the list doesn t matter. meaning D R A vehicle locked LOCKED driver door unlocked DRIVER all doors unlocked UNLOCKED alarm sounding ALARM ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 13 ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 14 Choice of Representation Affects Amount of Logic Needed As you may realize from your experience with bit-sliced designs, the representation does matter (for the amount of logic needed). We will talk more later about ways to choose. Use to Denote the Next State (in Next Clock Cycle) The + s in indicate that these are values in the next clock cycle. Let s rewrite the next- table with bits. The table gives us as a function of and inputs ULP. Such tables typically use binary order for s (vertical) and inputs (horizontal). We use Grey code order on both axes for convenience (in copying to K-maps). ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 15 ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 16
5 How to Fill in the Next-State Table Where should we start? ULP Let s make some design decisions first What about multiple buttons? Completing the Design Requires Decisions To fill in the next- table starting with only the abstract design, we need to make many design decisions, including some that we haven t even recognized yet. For example, What happens when the user presses more than one button? What happens when the user presses unlock in the UNLOCKED? ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 17 ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 18 Make Design Decisions Early When Possible Let s try to make decisions first. Design decisions can shape the design, and may conflict with one another. Making decisions early and writing them down ensures that any issues are raised early, and that known decisions are not overlooked (in which case the final design answers them implicitly, with no human guidance). Start by Deciding How to Handle Multiple Buttons We re going to start by prioritizing the buttons. Our rules: Panic has priority! Lock has second priority. Unlock only matters when neither of the others is pressed. ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 19 ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 20
6 Start with the Panic Button (Highest Priority) The next- table gives us ULP panic button pushed Continue with the Lock Button (Second Priority) The next- table gives us. ULP lock button pushed ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 21 ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 22 No Buttons? No Change. All Self-Loops What if the user pushes nothing? ULP no buttons pushed Finally, Unlock But are We Done? Two transitions were defined for Unlock. ULP from LOCKED What 01about these? from DRIVER ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 23 ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 24
7 We Have More Design Decisions to Make! What should happen if we press unlock when the car is already fully unlocked (in the UNLOCKED )? Maybe just stay UNLOCKED. What should happen if we press unlock while the alarm is sounding? Continue to lock out an attacker / thief? Or open the doors so that the owner can climb inside quickly? Let s Implement Our Decisions Ignore Unlock in both other cases. ULP from ALARM from UNLOCKED ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 25 ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 26 The Rest You Know How to Do The rest is K-maps, expressions, and logic. 1. Express and in terms of S 1, S 0, U, L, and P. 2. Express D, R, and A in terms of S 1, S Build the combinational logic. 4. Put the next expressions and into the D inputs of two flip-flops. You should do it as an exercise. Break up the truth tables or use 5-variable K-maps. One Last Tool: the Complete State Transition Diagram The complete transition diagram contains the information in both the list and the next- table. inputs for this transition ID / outputs ULP = _ STATE /DRA ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 27 ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 28
8 Complete State Transition Diagram ULP=000,x10 abbreviate as ULP = x00 ULP=xx1,x0x LOCKED 00/000 ULP=xx1 ALARM 01/001 ULP=x10 ULP=100 ULP=x10 ULP= x10 ULP=xx1 ULP=xx1 DRIVER 10/100 ULP=100 UN- LOCKED 11/110 ULP=000 ULP=000 or 100 Be Careful with Input Abbreviations Input abbreviations can render a transition diagram incomplete (if labels fail to cover all input combinations), or inconsistent (if labels indicate multiple next s). For example, self-loop from ALARM labeled ULP=xx1,x0x: the patterns x01 match both labels! In this case, these two combinations go to the same next, so it s ok. ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 29 ECE 120: Introduction to Computing 2016 Steven S. Lumetta. All rights reserved. slide 30
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