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Assembly Language Programming

Lesson 2: Enumeration

By Robert M (adapted by Duane Alan Hahn, a.k.a. Random Terrain)

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Page Table of Contents

Original Lesson

In lesson 1 we introduced the idea of a bit. We learned that a bit is the smallest piece of information in a computer. We learned that a bit can have either the value 1 or 0. We also learned that we as programmers can assign any meaning we wish to individual bits used by our program.


In this lesson we will look at the important programming practice of enumeration.


  1. To count off or name one by one; list: A spokesperson enumerated the strikers' demands.
  2. To determine the number of; count.

Let's say you want the to write a computer game where the player is picking fruit. There are 4 kinds of fruit in the game: Apples, Oranges, Bananas, and Cherries. All 4 kinds of fruit can be on the screen at the same time. Therefore, your program must keep track of each piece of fruit on the screen, and remember what kind of fruit it is so that it can draw the fruit correctly, and award the correct points to the player when they pick the fruit.


The easiest way to track the different kinds of fruit is to enumerate them:


All information in a computer is stored in bits so let's convert that to a bit:


Uh oh! We have run out values to enumerate our fruit because a bit can only be 0 or 1. To enumerate the fruit we will have to combine 2 bits together like this:


The 2 bits together have 4 possible combinations so we can enumerate the fruits in our program using 2 bits for each piece of fruit.


What if our program needs to have 8 different kinds of fruit, how many bits do we need then?


The answer is 3 bits. 3 bits together have 8 value combinations:


The formula for the number of combinations possible given N bits is:


So an enumeration of W items will require a minimum of:







Here are some real world examples of enumeration from Atari 2600 games. For each item calculate the minimum bits the program must use to keep track of the particular piece of information.

  1. The cartridge combat has 27 game variations, what is the minimum number of bits the combat program can use to keep track of the current variation?
  2. The 112 game variations for Space Invaders.
  3. The Atari 2600 Display is 160 pixels horizontally by 192 pixels vertically (NTSC) To position a player on the screen you must enumerate its horizontal and vertical position. How many bits are needed to store the horizontal and vertical positions of the player?
  4. In Surround, the "arena" is 40 blocks wide by 20 blocks high. Each block in the playfield is either filled or empty. How many bits are needed to remember the status of the playfield? How many bits are needed to remember the horizontal and vertical position of each player?







  1. The cartridge combat has 27 game variations, what is the minimum number of bits the combat program can use to keep track of the current variation?
  2. 2^5 = 32 >= 27, so 5 bits are necessary.



  3. The 112 game variations for Space Invaders.
  4. 2^7 = 128 >= 112, so 7 bits are necessary.



  5. The Atari 2600 Display is 160 pixels horizontally by 192 pixels vertically (NTSC) To position a player on the screen you must enumerate its horizontal and vertical position. How many bits are needed to store the horizontal and vertical positions of the player?
  6. 2^8 = 256 >= 192 >= 160, so 8 bits are needed for each horizontal or vertical position. 16 bits total.



  7. In Surround, the "arena" is 40 blocks wide by 20 blocks high. Each block in the playfield is either filled or empty. How many bits are needed to remember the status of the playfield? How many bits are needed to remember the horizontal and vertical position of each player?
  8. Since each block of the area has one of 2 states (filled or empty), we need a bit for each block.


    Number of Blocks = 40 * 20 = 800 bits needed for the arena.


    2^6 = 64 >= 40 so 6 bits are needed to store each player's horizontal position.


    2^5 = 32 > = 20 so 5 bits are needed to store each player's vertical position.

    EricBall said:

    Note: 3 & 4 have two answers depending on whether you are describing width & height independently or not. Bonus marks if you give both answers.

    This is true.


    For problem 3, we could enumerate all the pixels on the screen (160 x 192 = 30720 possible positions):


    2^15 = 32767 >= 30720, so you could store the player's position using 15 bits instead of 16 as required for storage of separate X and Y coordinates.


    For problem 4, we could do the same trick for storing the player positions:


    2^10 = 1024 >= 800, so you could store each player's position using 10 bits instead of the 11 needed to store X and Y positions separately.


    You may be wondering why then would you not always use the method of storage that uses the fewest bits? The answer is that the code of the program must process the data in the format that you choose, and it is easier to write code for separate X and Y coordinates than it is to write code for single enumerated position. In assembly language programming you will find there are many tricks that can be performed by using exotic data formats. I will provide examples much later in the course.

    EricBall said:

    Just to elaborate on the reasons why more bits than necessary may be used:

    • If the two values are independent (e.g. X & Y positions), so they are typically updated or used/tested separately.
    • Standard word lengths are easier to manipulate (e.g. 1 byte = 8 bits).
    • Combining/extracting multiple variables requires multiplication/division, which is typically not efficient (e.g. position = Y * 160 + X, or X = position MOD 160).
    • Room for expansion/enhancement.




Other Assembly Language Tutorials

Be sure to check out the other assembly language tutorials and the general programming pages on this web site.


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Lesson Links

Lesson 1: Bits!

Lesson 2: Enumeration

Lesson 3: Codes

Lesson 4: Binary Counting

Lesson 5: Binary Math

Lesson 6: Binary Logic

Lesson 7: State Machines





Useful Links

Easy 6502 by Nick Morgan

How to get started writing 6502 assembly language. Includes a JavaScript 6502 assembler and simulator.



Atari Roots by Mark Andrews (Online Book)

This book was written in English, not computerese. It's written for Atari users, not for professional programmers (though they might find it useful).



Machine Language For Beginners by Richard Mansfield (Online Book)

This book only assumes a working knowledge of BASIC. It was designed to speak directly to the amateur programmer, the part-time computerist. It should help you make the transition from BASIC to machine language with relative ease.



The Second Book Of Machine Language by Richard Mansfield (Online Book)

This book shows how to put together a large machine language program. All of the fundamentals were covered in Machine Language for Beginners. What remains is to put the rules to use by constructing a working program, to take the theory into the field and show how machine language is done.



6502 Instruction Set with Examples

A useful page from Assembly Language Programming for the Atari Computers.

Continually strives to remain the largest and most complete source for 6502-related information in the world.



Guide to 6502 Assembly Language Programming by Andrew Jacobs

Below are direct links to the most important pages.



Stella Programmer's Guide

HTMLified version.



Nick Bensema's Guide to Cycle Counting on the Atari 2600

Cycle counting is an important aspect of Atari 2600 programming. It makes possible the positioning of sprites, the drawing of six-digit scores, non-mirrored playfield graphics and many other cool TIA tricks that keep every game from looking like Combat.



How to Draw A Playfield by Nick Bensema

Atari 2600 programming is different from any other kind of programming in many ways. Just one of these ways is the flow of the program.



Cart Sizes and Bankswitching Methods by Kevin Horton

The "bankswitching bible." Also check out the Atari 2600 Fun Facts and Information Guide and this post about bankswitching by SeaGtGruff at AtariAge.



Atari 2600 Specifications

Atari 2600 programming specs (HTML version).



Atari 2600 Programming Page (AtariAge)

Links to useful information, tools, source code, and documentation.




Atari 2600 programming site based on Garon's "The Dig," which is now dead.



TIA Color Charts and Tools

Includes interactive color charts, an NTSC/PAL color conversion tool, and Atari 2600 color compatibility tools that can help you quickly find colors that go great together.



The Atari 2600 Music and Sound Page

Adapted information and charts related to Atari 2600 music and sound.



Game Standards and Procedures

A guide and a check list for finished carts.




A multi-platform Atari 2600 VCS emulator. It has a built-in debugger to help you with your works in progress or you can use it to study classic games.




A very good emulator that can also be embedded on your own web site so people can play the games you make online. It's much better than JStella.



batari Basic Commands

If assembly language seems a little too hard, don't worry. You can always try to make Atari 2600 games the faster, easier way with batari Basic.



Atari 2600 BASIC

If assembly language is too hard for you, try batari Basic. It's a BASIC-like language for creating Atari 2600 games. It's the faster, easier way to make Atari 2600 games.

Try batari Basic

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In Case You Didn’t Know


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CO2 is Greening The Earth

The Climate Agenda



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Hydroxychloroquine = Good

Although some people with certain conditions may not be able to take it, hydroxychloroquine is a cheap drug that has been prescribed by doctors since the 1950s and it seems to be helping many people who have COVID-19 when administered early enough. (Hydroxychloroquine is also supposedly safe and tolerable as an anti-cancer therapy.) Seems like most news sources are going out of their way to make it sound like hydroxychloroquine is the most dangerous drug in the world, but they also make it sound like it’s the greatest drug in the world for lupus and rheumatoid arthritis patients. They basically say that using hydroxychloroquine for COVID-19 patients would be taking that great and wonderful drug away from the other patients who need it. So which is it? Is hydroxychloroquine deadly or divine?


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In case you didn’t know, Patrick Howley reported that one of the authors of the ‘study’ saying that hydroxychloroquine doesn’t work at VA hospitals got a research grant from Gilead (the company that makes remdesivir). Does that seem a little fishy to you?


Bryan Fischer said in an article that Dr. Fauci has known since 2005 that chloroquine is an effective inhibitor of coronaviruses. You might also want to check out the following three links:

The REAL Truth about Dr. Fauci, Remdesivir and Hydroxychloroquine!

Chloroquine Is a Potent Inhibitor of SARS Coronavirus Infection and Spread (2005)

Sequential CQ / HCQ Research Papers and Reports


“The Disruptive Physician” had this to say at Twitter: “Meanwhile, regular doctors like me are using HCQ + Azithromycin and Zinc to good effect. One nursing home in NE Ohio had 30 cases - started everyone on HCQ, no deaths. Quick recovery. Why would the MSM hide this? Why would twitter block people who question the WHO?” You might also want to check out Dr. Stephen Smith, Dr. Ramin Oskoui and Dr. Yvette Lozano.


In case you’re interested, here are a few COVID-19 patients who appear to claim that hydroxychloroquine saved their lives: elderly couple Louis Amen and Dolores Amen, Daniel Dae Kim, Rio Giardinieri, John McConnell, Margaret Novins, Jim Santilli, Billy Saracino, and Karen Whitsett (Democratic member of the Michigan House of Representatives).


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