4. Finite State Machines

4.1. Simple Coffee Vending Machine

In this experiment, we will develop a finite state machine (FSM) for a simple coffee vending machine. The machine provides a cup of freshly brewed coffee for 1 Euro. If a coin is inserted into the machine (we assume that only 1 Euro coins fit in the slot), the user can press a button to order the drink. Of course, if no money is provided, our machine should also not provide a drink. Also, since we are a greedy company, we do accept more coins but do not provide more than one coffee if the user has overpaid.

Table 4.1.1 State transition table for the simple coffee machine.

Current State	Input	Next State	Output
waiting for payment	coin	payment received	Switch light on informing user to press the button
	press	waiting for payment	None
payment received	coin	payment received	None
	press	waiting for payment	Brew a delicious coffee and go back to original mode

Tasks

1. Verify that Fig. 4.1.1 represents the state transition diagram

   

   Fig. 4.1.1 State transition diagram for the coffee vending machine.

   for the FSM described in Table 4.1.1.

2. Convince yourself that the abstract Mealy formulation in Table 4.1.2 with the following states

   1. S0 for the state waiting for payment

   2. S1 for the state payment received

   using the inputs

   1. A for the input coin inserted

   2. B for the input Button B pressed (coffee)

   and outputs

   1. Y1 for light on/off

   2. Y2 for brew one/no coffee

   satisfies our goals.

   Table 4.1.2 Mealy state transition table with outputs for the simple coffee machine.

   Current	Input		Next State	Output
   State	A	B		Y1	Y2
   0	1	X	1	0	0
   0	0	X	0	0	0
   1	X	0	1	1	0
   1	X	1	0	1	1

   NOTE: Any additional coin will be lost in the overpayment scenario if the user inserts money while pressing the button.

3. Verify the correctness of the boolean equations for the next state and the outputs in sum-of-product form

   (4.1.1)

4. Draw the following circuit using the Digital tool and check that it produces the correct outputs.

   

   Fig. 4.1.2 Circuit for the simple coffee machine.

   Hint

   You will find the clock in the menu (Bauteile/IO/Takteingang). It can be activated by right-clicking on it and checking the Echtzeittakt starten box. Also, you might want to use a release button (Bauteile/IO/Taster) for the inputs. Note that you might observe unexpected behaviour depending on how long you press the button.

4.2. Fair Coffee Vending Machine

Due to a large number of customer complaints, it was decided to change the overpayment policy and develop a finite state machine for a more fair coffee vending machine. As before, the machine has a slot that only accepts 1 Euro coins. However, the machine will now accept up to two coins before ordering a coffee and will return any excessive amount of coins. After inserting money, the user will have the option to order a small (1 Euro) or a LARGE coffee (2 Euro) by pressing the corresponding buttons B1 or B2, respectively.

The state transition table for the fair coffee machine is given in Table 4.2.1.

Table 4.2.1 State transition table for the fair coffee machine.

Current State	Input	Next State	Output
waiting for payment	coin	payment received	Switch on light to indicate that machine is ready to brew
	B1	waiting for payment	None
	B2	waiting for payment	None
payment received	coin	overpayment received	Keep light on
	B1	waiting for payment	Brew a small coffee and switch off light
	B2	payment received	None
overpayment received	coin	overpayment received	Return one coin
	B1	payment recived	Brew a small coffee
	B2	waiting for payment	Brew a LARGE coffee and switch light off

Tasks

1. Draw a state transition diagram for the FSM using the states

   1. S0 for the state waiting for payment

   2. S1 for the state payment received

   3. S2 for the state overpayment received

   using the inputs

   1. A for the input coin inserted

   2. B1 for the input Button B1 pressed (small coffee)

   3. B2 for the input Button B2 pressed (LARGE coffee)

2. Formulate the corresponding tables for the state transistion, the binary state encoding, and output encoding.

3. Write down the boolean equations for the next state and the outputs in sum-of-product form.

4. Implement the circuit in the Digital tool.

   

   Fig. 4.2.1 Incomplete circuit for the fair coffee machine.

   Hint

   AND, OR, … logic gates can have more than two inputs. To change the number of inputs, you need to right-click on the gate and set Anzahl der Eingänge to the desired value.

5. Test your circuit and validate that it produces the correct outputs.

6. Save and submit the state transition diagram (as fair_coffee_machine.svg), the tables for the state transistion (as fair_coffee_machine_transition.csv), the binary state encoding (as fair_coffee_machine_encoding.csv), and output encoding (as fair_coffee_machine_output.csv) besides a txt-file with the boolean equations (as fair_coffee_machine.txt) and the circuit (as fair_coffee_machine.dig).

4.3. Fancy Coffee Vending Machine

The fair coffee machine was a big success and most customers are happy. However, there are still some people who would like to enjoy a fancy Latte Macchiato. Thus, the company has decided to also offer this option at a price of 3 Euros and design a new vending machine. The new machine now accepts up to three coins before ordering a coffee and will return any excessive amount of coins. After inserting (sufficient) money, the user will have the option to order a small (1 Euro), a LARGE coffee (2 Euro), or a fancy Latte Macchiato by pressing the corresponding buttons B1, B2, or B3, respectively.

Your task is to extend the state transition table in Table 4.2.1 by appropriate states, inputs and outputs to achieve this goal.

Tasks

1. Draw a state transition diagram for the FSM of the fancy coffee maschine.

2. Formulate the corresponding tables for the state transistion, the binary state encoding, and output encoding.

3. Write down the boolean equations for the next state in sum-of-product form.

4. Implement the circuit in the Digital tool.

   

   Fig. 4.3.1 Incomplete circuit for the fancy coffee machine.

5. Test your circuit and validate that it produces the correct outputs.

6. Save and submit the state transition diagram (as fancy_coffee_machine.svg), the tables for the state transistion (as fancy_coffee_machine_transition.csv), the binary state encoding (as fancy_coffee_machine_encoding.csv), and output encoding (as fancy_coffee_machine_output.csv) besides besides a txt-file with the boolean equations (as fancy_coffee_machine.txt) and the circuit (as fancy_coffee_machine.dig).