By Robert M (adapted by Duane Alan Hahn)
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.
e·nu·mer·ate
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:
Apple = 0
Orange = 1
Banana = 2
Cherries = 3
All information in a computer is stored in bits so let's convert that to a bit:
Apple = 0
Orange = 1
Banana = ??
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:
Apple = 00
Orange = 01
Banana = 10
Cherries = 11
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:
000
001
010
011
100
101
110
111 = 8 combinations.
The formula for the number of combinations possible given N bits is:
combinations = 2 ^ N = (2 to the power of N)
So an enumeration of W items will require a minimum of:
N = log_{2}(W)
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.
2^5 = 32 >= 27, so 5 bits are necessary.
2^7 = 128 >= 112, so 7 bits are necessary.
2^8 = 256 >= 192 >= 160, so 8 bits are needed for each horizontal or vertical position. 16 bits total.
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:
Other Assembly Language Tutorials
Be sure to check out the other assembly language tutorials and the general programming pages on this web site.


Lesson 2: Enumeration
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 parttime computerist. It should help you make the transition from BASIC to machine language with relative ease.
The 6502 Instruction Set broken down into 6 groups.
Nice, simple instruction set in little boxes (not made out of tickytacky).
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.
An easytoread page from The Second Book Of Machine Language.
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 6502related information in the world.
By John Pickens. Updated by Bruce Clark.
Guide to 6502 Assembly Language Programming by Andrew Jacobs
Below are direct links to the most important pages.
Goes over each of the internal registers and their use.
Gives a summary of whole instruction set.
Describes each of the 6502 memory addressing modes.
Describes the complete instruction set in detail.
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 sixdigit scores, nonmirrored 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 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.
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.
A guide and a check list for finished carts.
A multiplatform Atari 2600 VCS emulator. It has a builtin 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.
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.
Disclaimer
View this page and any external web sites at your own risk. I am not responsible for any possible spiritual, emotional, physical, financial or any other damage to you, your friends, family, ancestors, or descendants in the past, present, or future, living or dead, in this dimension or any other.
Use any example programs at your own risk. I am not responsible if they blow up your computer or melt your Atari 2600. Use assembly language at your own risk. I am not responsible if assembly language makes you cry or gives you brain damage.