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Assembly Language Programming

Lesson 3: Codes

By Robert M (adapted by Duane Alan Hahn)

Table of Contents

Original Lesson

In lesson one we learned what a bit is. In lesson 2 we learned how to use bits to enumerate lists of items. In this lesson we are going to learn how to use bits to encode information.

 

 

 

 

Definitions

Before we study codes, however, we need to take a detour and learn some new terminology. When we enumerated, we saw that with 1 bit we can enumerate 2 items 0 and 1. With 2 bits we can enumerate up to 4 items 00, 01, 10 and 11. So on and so on, such that given N bits we can enumerate up to 2^N items. As you can guess, it is a very common practice to combine bits together for the purpose of enumeration. Some combinations are used so frequently in programming that they have been given special names:

 

 

I will be using these terms in all future lessons so get comfortable with them now. For example the Atari 2600 has 128 bytes of RAM. How many bits is that? ANSWER: 128 bytes * 8 bits/byte = 1024 bits. What is RAM? Don't worry I will explain that in a later lesson.

 

If you are sharp eyed you may have noticed something about the naming of the bit strings above. Except for the octet each one is a power of 2! 2^0=1 (bit), 2^1=2(no name), 2^2=4(nybble), 2^3=8(byte), 2^4=16(word). This is no accident. Computers are based on bits and manipulate bits hence powers of two are a natural occurrence in digital computers. So these numbers appear very often in programming. As a programmer you will find there are advantages to using powers of 2 in your programming. The odd Octet will become clear in Lesson 4.

 

 

 

 

 

Introduction to Codes

All enumerations are codes, but not all codes are enumerations. What does that mean? It means that enumerations are one type of binary code. In lesson 2, we enCODEd the type of fruit (Apple, orange, banana, cherry) using bits. What makes enumerations special codes is that they exactly match the binary numbering system used in computers for arithmetic so: Apple = 00 = zero, orange = 01 = one, banana = 10 = two, cherry = 11 = three. We don't have to encode our types of fruit that way we could encode them as Apple = 10110, Orange = 10000, bandana = 10111, cherry = 11000, but this is now a code and not an enumeration.

 

 

 

 

 

 

 

 

Exercises

  1. Covert the following decimal numbers to BCD format:
    1. 10
    2. 253
    3. 7689
    4. 4

     

  2. Give an example of a 3 bit Gray code. Note: There is more than 1 correct answer.
  3. How many nybbles are there in a word?
  4. How many bits are in 512 bytes?
  5. How many octets are in 72 nybbles?
  6. You wish to store strings in your program. The strings will contain only capital letters A-Z, spaces, periods, question marks, and a special character that marks the end of the string. How many bits are needed to store each character in a string? By packing the character codes together how many characters could fit into 8 bytes?

 

 

 

 

 

Answers

  1. Covert the following decimal numbers to BCD format:
    1. 10 = 0001 0000
    2. 253 = 0010 0101 0011
    3. 7689 = 0111 0110 1000 1001
    4. 4 = 0100

     

     

  2. Give an example of a 3 bit Gray code. Note: There is more than 1 correct answer.
  3. Here's a way to make a gray code of any length of bits. Start with a gray code for 1 bit =

    0

    1

     

    To get a gray code of n+1 bits from a gray code of n bits simply repeat the n code followed (or preceded) by a single zero, then repeat the n code again in reverse followed by a single 1.

    So from the above one bit code we get a two bit code as

    0+0 = 00

    1+0 = 10

     

    Repeat 1 bit code in reverse.

    1+1 = 11

    0+1 = 01

     

    Simply repeat this process to get a 3 bit gray code:

    00+0 = 000

    10+0 = 100

    11+0 = 110

    01+0 = 010

     

    Repeat 2 bit code in reverse...

    01+1 = 011

    11+1 = 111

    10+1 = 101

    00+1 = 001

     

     

  4. How many nybbles are there in a word?
  5. We know how many bits are in nybble and a word so we can convert from one to the other by converting words to bits and then bits to nybbles.

     

    1 word = 16 bits

    1 nybble = 4 bits

     

    nybbles per word = 16/4 = 4 nybbles.

     

     

  6. How many bits are in 512 bytes?
  7. By our definitions there are 8 bits in a byte. So there will be:

     

    512 * 8 = 4096 bits in 512 bytes.

     

     

  8. How many octets are in 72 nybbles?
  9. Again we will convert from one unit to bits, and then from bits to the other unit.

     

    72 nybbles * 4 (bits per nybble) = 288 bits

     

    288 bits / 3 bits per octet = 96 octets.

     

     

  10. You wish to store strings in your program. The strings will contain only capital letters A-Z, spaces, periods, question marks, and a special character that marks the end of the string. How many bits are needed to store each character in a string? By packing the character codes together how many characters could fit into 8 bytes?
  11. First we count the total number of symbols possible for each character. A-Z is 26 symbols. Space, period, question mark, and termination are 4 more symbols. 26 + 4 = 30 total possible symbols.

     

    We can enumerate the symbols as we learned in lesson 2. The number of bits needed is

     

    log(base2) 30 rounded up = 5 bits are needed per symbol in the string!

     

    Now the second part of the question asked how many symbols will fit into 8 bytes worth of bits.

     

    total bits = 8 bits per byte * 8 bytes = 64 bits.

     

    Number of symbols in 8 bytes = 64 bits / 5 bits per symbol = 12.8 symbols

     

    Not quite 13 symbols will fit into 8 bytes of space.

 

 

 

Other Assembly Language Tutorials

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

 

 

< Previous Lesson

 

 

Next Lesson >

 

 

 

 

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.

 

 

6502.org

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.

 

 

MiniDig

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.

 

 

Stella

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.

 

 

JAVATARI

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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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.

 

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