Robert M Posted May 15, 2011 Share Posted May 15, 2011 Okay, so somebody reminded me I never finished my assembly language programming courses. Here is the next one after a five year hiatus. My bad Assembly Language Programming Lesson 7 - State Machines: ========================== Written by Robert Mundschau in May 2011. ----- The last topic we must cover before we can discuss programming the 6507 with assembly langauge is state machines. You need to understand state machines, because the 6507 microprocessor is a state machine. when you understand the rules for state machines, assembly language programming (all programming really) will make more sense. At the root, state machines are abstract mathematical constructs. What is special about state machines is that they can be implemented as real mechanical or electronic machines. We will show that a state machine can impose a set of logical control or rules onto a system. This control makes the real-world device predictable and useful. A state machine is a list of states, a list of possible inputs, and a matrix of next states for each current-state/input combination. For a really simple real world example consider an electric light connected to and on/off switch. In our imaginary perfect world we can simplfy the state machine to the following: SIMPLE LIGHT SWITCH: -------------------- Lists of States: ( LIGHT_ON , LIGHT_OFF ) List of Inputs: ( SWITCH_UP, SWITCH_DOWN ) Table of Transitions: | Input: current state: | SWITCH_UP | SWITCH_DOWN +-------------+------------- LIGHT_ON | LIGHT_ON | LIGHT_OFF <<== The cells of the table ------+-------------+------------- contain the next state. LIGHT_OFF | LIGHT_ON | LIGHT_OFF To understand this state machine, consider you have the current state of LIGHT_ON or LIGHT_OFF, and given an input of SWITCH_UP or SWITCH_DOWN you find the cell in the matrix that corresponds to the combination of the two. The contents of the matching cell in the table is the new state of the machine following the given input. All input to a state machine is processed one input at a time in the order the inputs happened. We wil tackle the problem of simultaneous inputs later, assume for now that can not happen. We have modeled a simple light switch. We ignored real-world details to simplify the model down to its bare essentials. We assumed a perfect electrical supply to the system, and don't worry whether the bulb could burn out. An infinite number of inputs exist to any real-world system. As a programmer you will need to learn to elimnate inputs you don't need to worry about in your design. Or which will be handled elsewhere in the system. Hitting an atari with a baseball bat is an input to the system, but I doubt you will bother trying to write any code to deal with that potential input. A broken joystick reporting both left and right directions at the same time, however, is a very real input to consider. Will the state machine of your game program handle that input? Does it need to? As a programer you need to consider all reasonable inputs or your game may act glitchy or provide cheats to the player you never intended. Using state machines in your game design is a useful way to control player interaction with the system. When you see video game glitches it can be because an input/state combination occurred that the programmer did not account for in their design and implementaion. ----- Now lets examine a slightly more complex and useful state machine. Imagine a simple gumball vending machine. The machine will only take pennies. The machine has a vend button, and has the ability to detect when it is empty. If a user inserts a penny and presses the vend button, the machine will vend one gumball. If the user inserts a second penny, the first penny is returned. Any penny inserted while the machine is empty will be returned. Using these simple requirements we can generate the state machine design below. PENNY GUMBALL MACHINE: ---------------------- List of States: ( {starting state}WAITING, READY_TO_VEND, EMPTY ) List of Inputs: ( PENNY, VEND_BUTTON, EMPTY_SIGNAL ) Table of Transitions: | Input: Current State: | PENNY | VEND_BUTTON | EMPTY_SIGNAL | +-----------------+---------------+--------------+ WAITING |READY_TO_VEND | WAITING | EMPTY | < next state exit action | none | none | none | < extra work --------------+-----------------+---------------+--------------+ READY_TO_VEND |READY_TO_VEND | WAITING | EMPTY | exit action | return penny | vend gumball | return penny | --------------+-----------------+---------------+--------------+ EMPTY |EMPTY | EMPTY | EMPTY | exit action | return penny | none | none | There are three big differences between this state machine and the first state machine we looked at: 1. It has more states and inputs than the first example. A state machine can have any number of states and inputs, and they do not have to be the same number of each. 2. In the list of states I marked the WAITING state at the {starting state}, which means the state machine is in the WAITING state when it starts running. If you don't specify a starting state for your state machine, it can start in any state which may cause unwanted behavior. For the light switch example the starting state didn't matter. 3. In the cells of the state transition table I added an exit action to be performed before transitioning to the new state. The addition of actions changes the state machine into something useful. Our design has three possible exit actions which we could add to the design as a list like this: List of Exit Actions: ( none, return penny, vend gumball). To operate this state machine, when an input arrives the following happens: 1. Lookup the the transition table entry corresponding to the current state and the input. 2. Perform the exit action in that table entry. 3. Change the current state to the next state in that table entry. Using this algorithm the exit actions represent real world interactions with the user. The underlying state machine acts as the controller to limit the interactions with the user to the correct order. The user must insert a penny and then press the vend button to receive a gumball. Pressing vend and then inserting a penny will not yield a gumball. The Penny Gumball Machine example uses exit action items to join the logical control aspects of an state machine to real world interactions with the user. You can imagine that the actions "return penny" and "vend gumball" are implemented with a mechanism activated by the mechanical or electronic device that implements the state machine logic. Hopefully, it is clear now why state machines are so useful. ---- You can tie actions to more than just the exit from a given state. There are three distinct places to attach actions to a state machine: 1. Exit Action - Performed on exiting the current state. (as above) 2. Transition Action - On the specific transition from current state to the next state. 3. Enter Action - On entering the next state. Any combination of the 3 actions can happen when the state machine processes an input. The listed order is the same order the actions will be taken during input processing. First, the Exit Action is performed. Second, the Transition Action is performed. The state is changed to the new state, and lastly the Enter Action for the new state is performed. Hopefully, the operation of the Exit Action and Enter Action are clear, but the Transition Action may be harder to grasp at first. A transition action can be different for every combination of current and next states that can be made from the List of States. We can show all the combinations of current and next states as a 2-dimensional matrix with the current state on the rows and the next state on the columns. The cells of the matrix hold the Transition Action. Below is an example of the Transition Action Table for the Simple Gumball Machine. Imagine we delete the Exit Actions in the original design and replace them with these Transistion Actions. Table of Transition Actions: | Next State: Current State: | WAITING | READY_TO_VEND | EMPTY | +---------------+---------------+--------------+ WAITING | none | none | none | <= Actions --------------+---------------+---------------+--------------+ NOT READY_TO_VEND | vend gumball | refund penny | refund penny | States! --------------+---------------+---------------+--------------+ EMPTY | none | none | none | This alternate approach is almost identical to the original design. It does not handle the case, however, where the user inserts a penny into an empty machine. Using this alternate approach that case would result in the user losing their penny. Do not take from this limited example that exit actions are somehow superior to transition actions or entry actions. Each kind of action serves a different purpose and can be equally useful. Often state machines will use a fairly complex combination of the different kinds of actions to model complex behavior with a relatively simple design. ---- At the start of the lesson I indicated that the 6507 microprocessor is a state machine, and we will examine that state machine in detail next lesson. Right now it is important to recognize that as a programmer you can use state machines to help you writing your game code. You can use state machines in your code to simplify your work. Try to break your game into its actors and see if the state machine paradigm can be applied to them. Once we start looking at real code, we will return to state machines to see how they are really implemented. State machines can be nested and interact with each other. For example, an given action may be to generate an input to one or more other state machines. Or a state machine may only be allowed to process input when another state machine is in the correct state. When applying the state machine paradigm to a game element try to map states to a high level framework of control. For example, you probably don't want a separate state for an object moving in each possible direction if the constraints for motion are the same in all directions. Rather, a single state of IN_MOTION combined with some other infomration about direction and speed stored elsewhere will yield a cleaner design. Let's take a look at an example state machine for an existing video game object. Consider the "square" hero from the Atari game Adventure, and how we might describe the state machine that limits the user's control of this character in the game. List of States: OFF: This is the starting state at the game select screen. ACTIVE: The hero is free to move. DEAD: The hero is in the stomach of an dragon. WINNER: The player has won the game. No more motion allowed. List of Inputs: SELECT: The player pressed the select switch. RESET: The player pressed the reset switch. CHOMP: A dragon has swallowed the player. VICTORY: The chalice is in the gold castle. State Transition Table Current | Input: State: | SELECT | RESET | CHOMP | VICTORY ----------+----------+----------+-----------+---------- OFF | OFF | ACTIVE | OFF {*} | OFF {*} ----------+----------+----------+-----------+---------- ACTIVE | OFF | ACTIVE | DEAD | WINNER ----------+----------+----------+-----------+---------- DEAD | OFF | ACTIVE | DEAD | WINNER{*} ----------+----------+----------+-----------+---------- WINNER | OFF | ACTIVE | WINNER{*} | WINNER{*} ----------+----------+----------+-----------+---------- The transistions marked with {*} should never occur. In the real game there is logic to prevent the player from being eaten after winning the game. Its helpful to consider these unexpected interactions in your game designs. Can you think of some actions to attach to this state machine? Clearly the RESET input should change the position of the hero in the game world. Can you imagine a state machine to handle the player carrying and dropping game objects? ---- As a last note, we have considered so far that only one input can happen at a time. In the real world it is possible for inputs to happen simultaneously. Or if not exactly at the same time, then within the time it takes for the state machine to come finish processing one input and getting a chance to process another input. For example, the user can press the select and reset switches at roughly the same time. As a programmer you must deal with simultaneous inputs in one of two main ways: 1. Assign a different priority to all inputs. The highest priority input is always handled first. Lower priority inputs are handled after, or ignored. 2. Create a new input that is a combination of multiple inputs. So if SELECT and RESET are pressed at the same time, the input to the system becomes SELECT_AND_RESET. This approach can cause the number of inputs to balloon exponentially if applied liberally. It can be really useful on a limited basis. ============================================================================ Exercises: ---------- 1. Generate a state machine for a light with two control switches. Changing the position of either switch will toggle the light on/off. Assume only one switch can change at any time. Provide the lists of states, inputs and transitions. 2. Add a "REFUND" input to the PENNY GUMBALL MACHINE specification above to let the user get their penny back. 3. BONUS CHALLENGE: Pick an element of an existing Atari VCS game and create a state machine for the behavior of the element. 2 Quote Link to comment Share on other sites More sharing options...
ScumSoft Posted May 15, 2011 Share Posted May 15, 2011 Better late than never? Quote Link to comment Share on other sites More sharing options...
+Random Terrain Posted May 24, 2011 Share Posted May 24, 2011 An adapted version of lesson 7, along with the rest of the lessons so far, can be viewed here: www.randomterrain.com/atari-2600-memories.html#assembly_language Quote Link to comment Share on other sites More sharing options...
jdrose Posted January 4, 2012 Share Posted January 4, 2012 Great article. Quote Link to comment Share on other sites More sharing options...
Sheddy Posted January 8, 2012 Share Posted January 8, 2012 Quote Link to comment Share on other sites More sharing options...
+Random Terrain Posted May 12, 2019 Share Posted May 12, 2019 Can somebody who knows assembly language post the answers to the exercises? Exercises:----------1. Generate a state machine for a light with two control switches. Changingthe position of either switch will toggle the light on/off. Assume only oneswitch can change at any time. Provide the lists of states, inputs andtransitions.2. Add a "REFUND" input to the PENNY GUMBALL MACHINE specification above to letthe user get their penny back.3. BONUS CHALLENGE: Pick an element of an existing Atari VCS game and createa state machine for the behavior of the element. I'd like to put the answers on this page: randomterrain.com/atari-2600-memories-tutorial-robert-m-07.html Thanks. Quote Link to comment Share on other sites More sharing options...
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