Electronics II Physics 3620 / 6620

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Electronics IIPhysics 3620 / 6620

• Jan 28, 2009
• Part 1
• Finite State Machine (continued)

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Example I Even or odd

• The following machine determines whether the
  number of As in a string is even or odd
• A circles represents a state (also known as a
  vertex) an arrow (or arc) represents a
  transition

• This is an example of a State Diagram
• In Labview we represent different states using
  the case structure
• Inputs are the characters of a string
• The output is the resultant state see in-class
  example implemented in Labview (even_odd.vi)

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Labview Implementation

• Implementation in Labview is based on a case
  structure (whi8ch represents the state machine
  itself, and a while-loop around it

• The actual state is kept by a shift register
  within the while loop
• The shift register shows up as an input
  (initialize) and output pair

Programming ? Numeric ? Enum Const,.

• In some cases you can specify an exit state (as
  shown) to stop

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State Transition

• There are different methods to determine which
  state to transition to next. Four common methods
  are discussed below (Note in the following
  method examples, Init could transition to any
  state)

• Case 2 the init state has two possible
  transitions, Shut Down or Power Up.

• Case 1 the Init state that has only one
  possible transition.

Programming ? Comparison ? Select
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More Cases

• Case 4
• Init state using an inner loop and case
  structure to transition to the next state. The
  inner case structure contains one diagram for
  each transition that leaves the current state.
  Each of the cases in the inner case structure has
  two outputs a boolean value, which specifies
  whether or not the transition should be taken,
  and an enumerated constant, which specifies the
  state to which the transition goes. By using the
  loop index as an input to the case structure,
  this code effectively runs through each
  transition case one by one, until it finds a
  diagram with a True boolean output. After the
  True boolean output is found, the case outputs
  the new state to which the transition goes.
  Though this method may appear slightly more
  complicated than the previous methods, it does
  offer the ability to add names to transitions by
  casting the output of the loop index to an
  enumerated type. This benefit allows you to add
  automatic documentation to your transition
  code.

• Case 3
• Init state using a boolean array along with an
  array of enum constants. There is a boolean in
  the boolean array corresponding to each
  transition Init can make. The array of enum
  constants represents each transition name. The
  index of the first True boolean in the boolean
  array corresponds to the index of the new state
  in the array of enums.
• See programming ? Arrays ? to see the different
  types of arrays

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Error states

• Some state machines may have a error state with
  the following characteristics
• An unexpected input will cause a transition to
  the error state
• All subsequent inputs cause the state machine to
  remain in the error state

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Simplifying State Diagrams I

• State machines can get pretty complicated
• We can simplify the State Diagram by leaving
  out the error state
• The error state is still part of the machine
• Any input without a transition on our drawing is
  assumed to go to the error state
• Another simplification Use to indicate all
  other characters
• This is a convention when drawing the machineit
  does not mean we look for an asterisk in the
  input

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Example II Nested parenthesis

• The following example tests whether parentheses
  are properly nested (up to 3 deep)

• How can we extend this machine to handle
  arbitrarily deep nesting?

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Nested parentheses II

• Question How can we use a state machine to check
  parenthesis nesting to any depth?
• Answer We cant (with a finite number of states)
• We need to count how deep we are into a
  parenthesis nest 1, 2, 3, ..., 821, ...
• The only memory a pure state machine has is
  which state it is in
• However, if we arent required to use a pure
  state machine, we can add memory (such as a
  counter) and other features

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Nested parentheses III

• This machine is based on a state machine, but it
  obviously is not just a state machine

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Example from NI Coke Machine

• Specifications
• This application has the following requirements
• All Coke products are sold for 50 cents (This was
  still true on campus in 2004)
• The machine only accepts nickels, dimes, and
  quarters.
• Exact change is not needed.
• Change can be returned at anytime during the
  process of entering coins.

• The States
• 1.) INIT initialize our Coke Machine2.) WAIT
  FOR EVENT where the machine waits for coins3.)
  RETURN CHANGE where the machine returns
  change4.) COKE PRODUCT when the machine has
  received 50 or more cents it will dispense the
  beverage5.) QUARTER when the customer enters a
  quarter6.) DIME when the customer enters a
  dime7.) NICKLE when the customer enters a
  nickel8.) EXIT after the change is returned
  and/or beverage dispensed, the machine will power
  down (application will terminate)

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The State Diagram
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Mealy and Moore machines

• Moore machine
• Associates its outputs with states
• The outputs are represented either within the
  vertex corresponding to a state or adjacent to
  the vertex
• Mealy machine
• Associates its outputs with the transitions
• In addition to the input values, each arc also
  shows the output values generated during the
  transition the format of the label of each arc
  is Inputs/Outputs
• Both can be used to represent any sequential
  system and each has its advantages.

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Example Alarm clock state table
Present State Alarm Weekday Next State Turn off alarm
Asleep On X Awake in bed Yes
Awake in bed Off Yes Awake and up No
Awake in bed Off No Asleep No

• When you are asleep and alarm goes on, you go
  from being asleep to being awaked in bed you
  also turn off the alarm
• The next two rows encode your actions
• You get up
• You go back to sleep
• This table doesnt cover what you wouldnt
  do(i.e. if you are asleep and the alarm doesn't
  go off, you remain asleep, etc..)

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Alarm clock state table
Present State Alarm Weekday Next State Turn off alarm
Asleep Off X Asleep No
Asleep On X Awake in bed Yes
Awake in bed On X Awake in bed Yes
Awake in bed Off Yes Awake and up No
Awake in bed Off No Asleep No
Awake and up X X Awake and up No

• Covers all the cases
• First row covers the situation you are asleep,
  the alarm doesnt go off and you remain asleep
• Last row covers the situation you are awake and
  up and you remain awake and up
• The third row covers the case you are already up
  and the alarm goes off. You turn it off and
  remain Awake in bed

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Moore machine diagram

• Self arcs can be missing (since it outputs are
  associated with the states and not with the arcs)
• Offers a simpler implementation when the output
  values depend only on the state and not on the
  transitions
• It requires less hardware to produce the output
  values than does a Mealy machine, since its
  outputs depend only on its state and its input
  values
• It is well suited for representing the control
  units of microprocessors

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Mealy machine diagram

• Self arcs must be shown (because the output
  values are shown on the arcs)
• Can be more compact than Moore machine,
  especially when two or more arcs with different
  output values go into the same state