Home > Atari Memories > #Assembly > Assembly Language Programming

Assembly Language Programming

Lesson 4: Binary Counting

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

Tip Jar

As an Amazon Associate I earn from qualifying purchases. (I get commissions for purchases made through certain links on this page.)

Page Table of Contents

Original Lesson

In previous lessons, I have hinted that there is a standard method for counting using bits. In this lesson, I will introduce that standard method. First, I want to reiterate that this is NOT the only way to count using bits. It is simply the most common method, and therefore has considerable support for it built into most microprocessors including the 650X processor Family used in most classic gaming consoles and computers from the late 70s and 80s.






Numbering Systems

I must assume that if you can read the lessons in this class and understand them, then you must be familiar with decimal numbers and basic arithmetic like adding and subtracting. All decimal numbers are made using the ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. When you write a decimal number larger than 9 you must use two or more digits like this: 123 which is one hundred and twenty three. The 1 in 123 does not represent 1 it represents 100. The 2 in 123 is not 2 it is 20. The 3 in 123 does represent 3. Thus we call the 1 the hundreds digit, the 2 the tens digit, and 3 the one's digit. Each digit in a large decimal number represents that digit multiplied by a power of 10 based on its position and summed together.


Thus (1 * 10^2) + (2 * 10^1) + (3 * 10^0) = 100 + 20 + 3 = 123 Ta-da!


We count numbers inside computers exactly the same way except that the numbering system in computers does not have 10 digits, it only has 2 digits: 0 and 1 (bits!). The numbering system that uses only 0 and 1 is called the binary numbering system or simply binary. Since it only has 2 digits the value of each binary digit in a large binary number is multiplied by a power of 2 instead of a power of 10 as we do for decimal numbers.


The following table shows the positional value of the first 16 bits in the binary number system, as a power of 2. Note that the first position is numbered zero and not one.

     Bit position.


     |    Bit value

     |    |

   2^0  = 1        => bit

   2^1  = 2

   2^2  = 4        => octet

   2^3  = 8        => nybble

   2^4  = 16       

   2^5  = 32

   2^6  = 64

   2^7  = 128      => byte 

   2^8  = 256      

   2^9  = 512

   2^10 = 1024

   2^11 = 2048

   2^12 = 4096

   2^13 = 8192

   2^14 = 16384

   2^15 = 32768    => word

Every computer in the world has a limited number of bits. When you use binary numbers in a computer program, you must decide how many bits you will use to store each number that your program must keep track of. For 650X processors, the most common numbers of bits to use will be 8 (byte) and 16 (word) because the processor works with data an entire byte at a time for each instruction (see opcodes in lesson 3). You can use any number of bits, but since 8 and 16 are so common, we will focus on them for the remainder of this lesson. The same rules will apply to binary numbers made of any number of bits.


This should not seem strange, as you can use any number of digits to represent a decimal number. If you don't need all the digits, then your number will have 1 or more leading zeros.


0000123 is the 7-digit decimal number 123, by convention leading zeros are not shown for decimal numbers, but they are always present nonetheless. The same is true for binary numbers.


In the real world you can write as big of decimal number as your writing surface will allow. In a computer, your writing surface is bits. If you do not have enough bits allocated/available to store a binary number then your program can not store that number and the information will be lost. Such an event is called overflow if the number is too big, or underflow if the number is too small. We will examine overflow and underflow in detail in the next lesson.


You may be curious to know what is the biggest binary number you can store in a byte or a word. You already learned the formula in lesson 2enumeration. Given N bits, you can store 2^N different values. Counting positive integers starts at zero not one, so N bits can store binary numbers from 0 to (2^N)-1



A byte has 8 bits so N=8. Therefore, a byte can hold unsigned positive integers from 0 to (2^8)-1=256-1=255. From 0 to 255.










  1. Convert 213 to binary.
  2. Convert %00101100 to decimal.
  3. Convert 1087 to binary.
  4. Convert %1000010100011110 to decimal.
  5. Take the LSB from each of the numbers below, in order from top to bottom, to create a new binary number. The LSB from the first number in the list should be the LSB of the new number. The LSB of the last number in the list is the MSB of the new binary number. What is the new binary number? Now convert that number to decimal.
    1. %00110101








  6. For each of the numbers below, convert them to decimal twice. The first time assume that the numbers are in unsigned positive integer format. The second time assume that the numbers are in sign-magnitude format.
    1. %1000101
    2. %0101010
    3. %1100110
    4. %0000010


  7. What is the range of positive unsigned integers that can be stored in a word.



Bonus Questions:

  1. For each number a-d in problem 6, is each number signed or unsigned? (Hint: refer to lesson 1).
  2. Is the sign-magnitude format an Enumeration (lesson 2) or a code (lesson 3), and why?







  1. Convert 213 to binary.
     213 / 2 = 106 with a remainder of 1 ---------+
     106 / 2 = 53  with a remainder of 0 --------+|
     53 / 2  = 26  with a remainder of 1 -------+||
     26 / 2  = 13  with a remainder of 0 ------+|||
     13 / 2  = 6   with a remainder of 1 -----+||||
     6 / 2   = 3   with a remainder of 0 ----+|||||
     3 / 2   = 1   with a remainder of 1 ---+||||||
     1 / 2   = 0   with a remainder of 1 --+|||||||
                                          %11010101 binary = 213 decimal.



  3. Convert %00101100 to decimal.
        |||||||+--- 0 * 2^0 = 0 * 1   =   0
        ||||||+---- 0 * 2^1 = 0 * 2   =   0
        |||||+----- 1 * 2^2 = 1 * 4   =   4
        ||||+------ 1 * 2^3 = 1 * 8   =   8
        |||+------- 0 * 2^4 = 0 * 16 =   0
        ||+-------- 1 * 2^5 = 1 * 32  =  32
        |+--------- 0           
        +---------- 0
          0 + 0 + 4 + 8 + 0 + 32 + 0 + 0 = 44 decimal.



  5. Convert 1087 to binary.
  6. 1087 / 2 = 543 with a remainder of 1 543 / 2 = 270 with a remainder of 1

    270 / 2 = 135 with a remainder of 0

    135 / 2 = 67 with a remainder of 1

    67 / 2 = 33 with a remainder of 1

    33 / 2 = 16 with a remainder of 1

    16 / 2 = 8 with a remainder of 0

    8 / 2 = 4 with a remainder of 0

    4 / 2 = 2 with a remainder of 0

    2 / 2 = 1 with a remainder of 0

    1 / 2 = 0 with a remainder of 1

    So 1087 decimal = %10000111011 binary.



  7. Convert %1000010100011110 to decimal.
                 |    | |   ||||
                 |    | |   |||+---- 1 * 2^1 = 2
                 |    | |   ||+----- 1 * 2^2 = 4
                 |    | |   |+------ 1 * 2^3 = 8
                 |    | |   +------- 1 * 2^4 = 16
                 |    | +----------- 1 * 2^8 = 256
                 |    +------------- 1 * 2^10 = 1024
                 +------------------ 1 * 2^15 = 32768
          2+4+8+16+256+1024+32768 =  34078 decimal



  9. Take the LSB from each of the numbers below, in order from top to bottom, to create a new binary number. The LSB from the first number in the list should be the LSB of the new number. The LSB of the last number in the list is the MSB of the new binary number. What is the new binary number? Now convert that number to decimal.
    1. %00110101








    The LSB is the rightmost digit of each number, so the new binary number is: %1010111 which in decimal is: 64+0+16+0+4+2+1 = 87



  10. For each of the numbers below, convert them to decimal twice. The first time assume that the numbers are in unsigned positive integer format. The second time assume that the numbers are in sign-magnitude format.
    1. %1000101
    2. unsigned = 64 + 0 + 0 + 0 + 4 + 0 + 1 = 69 decimal

      signed = (-1) * (0 + 0 + 0 + 4 + 0 + 1 ) = -5 decimal


    3. %0101010
    4. unsigned = 0 + 32 + 0 + 16 + 0 + 2 + 0 = 50

      signed = (+1) * ( 32 + 0 + 16 + 0 + 2 + 0 ) = 50


    5. %1100110
    6. unsigned = 64 +32 + 0 + 0 + 4 + 2 + 0 = 102

      signed = (-1) * ( 32 + 0 + 0 +4 +2 +0 ) = -38


    7. %0000010
    8. unsigned = 2

      signed = 2



  11. What is the range of positive unsigned integers that can be stored in a word.
  12. There are two basic ways to solve this problem. I will demonstrate both because I think it's important to see the relationships that make both methods arrive at the same answer.


    1. The first approach is to realize that smallest unsigned integer is always zero. The binary value is unsigned so no bits are needed to store the sign of the number. In that case the largest unsigned number is the value of the binary number with all bits set to 1. A word has 16 bits, so the biggest unsigned binary number in a word is %1111111111111111.
    2. If we convert that to decimal we get:


      2^15 + 2^14 + 2^13 + 2^12 + 2^11 + 2^10 + 2^9 + 2^8 + 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0 =

      32768 + 16384 + 8192 + 4096 + 2048 + 1024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 65535.


    3. The second approach is to recall the formula from lesson 2 to find the maximum number of items that you can enumerate given N bits. The binary number system is just an enumeration of the natural numbers.

      combinations = 2 ^ 16 = 65536 combinations. Recall however that the enumeration begins at 0, so that leaves 65536 - 1 = 65535 as the largest possible unsigned integer in a word.



Bonus Questions:


  1. For each number a-d in problem 6, is each number signed or unsigned? (Hint: refer to lesson 1).
  2. This is a trick question. The correct answer is both. As we learned in the first lesson bits represent whatever you the programmer say that they represent. They can represent both at the exact same time. It doesn't matter, they are only bits. Meaning is given by you the programmer with the logic of your code.



  3. Is the sign-magnitude format an Enumeration (lesson 2) or a code (lesson 3), and why?
  4. It is a code because enumerations represent only positive values from 0 to N.






Note to Readers

We are rapidly descending from broad concepts to specific details in assembly programming. Most often, subsequent lessons will require an understanding of previous lessons. If you have questions after studying this material, do not hesitate to ask.




Other Assembly Language Tutorials

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


Amazon Stuff


< 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.

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

Back to Top



In Case You Didn’t Know


B Vitamins = Good

Some people appear to have a mental illness because they have a vitamin B deficiency. For example, the wife of a guy I used to chat with online had severe mood swings which seemed to be caused by food allergies or intolerances. She would became irrational, obnoxious, throw tantrums, and generally act like she had a mental illness. The horrid behavior stopped after she started taking a vitamin B complex. I’ve been taking #ad Jarrow B-Right for many years. It makes me much easier to live with.



Soy = Bad

Unfermented soy is bad! “When she stopped eating soy, the mental problems went away.” Fermented soy doesn’t bother me, but the various versions of unfermented soy (soy flour, soybean oil, and so on) that are used in all kinds of products these days causes a negative mental health reaction in me that a vitamin B complex can’t tame. The sinister encroachment of soy has made the careful reading of ingredients a necessity.



Wheat = Bad

If you are overweight, have type II diabetes, or are worried about the condition of your heart, check out the videos by William Davis and Ivor Cummins. It seems that most people should avoid wheat, not just those who have a wheat allergy or celiac disease. Check out these books: #ad Undoctored, #ad Wheat Belly, and #ad Eat Rich, Live Long.



Negative Ions = Good

Negative ions are good for us. You might want to avoid positive ion generators and ozone generators. Whenever I need a new air cleaner (with negative ion generator), I buy it from A plain old air cleaner is better than nothing, but one that produces negative ions makes the air in a room fresher and easier for me to breathe. It also helps to brighten my mood.



Litterbugs = Bad

Never litter. Toss it in the trash or take it home. Do not throw it on the ground. Also remember that good people clean up after themselves at home, out in public, at a campsite and so on. Leave it better than you found it.



Climate Change Cash Grab = Bad

Seems like more people than ever finally care about water, land, and air pollution, but the climate change cash grab scam is designed to put more of your money into the bank accounts of greedy politicians. Those power-hungry schemers try to trick us with bad data and lies about overpopulation while pretending to be caring do-gooders. Trying to eliminate pollution is a good thing, but the carbon footprint of the average law-abiding human right now is actually making the planet greener instead of killing it.


Watch these two YouTube videos for more information:

CO2 is Greening The Earth

The Climate Agenda



Hydrofracking = Bad

Hydrofracking is bad for you, your family, your friends, and the environment.



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?


If you believe that a couple of Trump supporters took the medicine hydroxychloroquine and it’s President Trumps fault that the husband died, you’ve been duped. Watch this video. The wife was a prolific Democratic donor, it seems she hated her husband, she used fish tank cleaner (not the medicine hydroxychloroquine), and now she is the subject of a homicide investigation.


Some people claim that the reason so many news sources want to keep doctors from using hydroxychloroquine for COVID-19 is that they are desperate to keep everyone afraid to leave their homes since mail-in voting will make voter fraud much easier (the only way they could beat Trump). Others claim that the rabid anti-hydroxychloroquine campaign was to make way for the expensive new drug called remdesivir. Drug companies can’t make much money with old generic drugs, so new drugs must be pushed. Both claims could be true since remdesivir supposedly isn’t as good as hydroxychloroquine.


According to Dr. Shiva Ayyadurai, hydroxychloroquine does four things: (1) stops viral entry, (2) stops viral RNA replication, (3) stops viral particle assembly, and (4) stops cytokine storm. Remdesivir only stops viral RNA replication. Did you get that? Hydroxychloroquine does four things and remdesivir only does one. The doctor also said that nearly 70 percent of the people who took remdesivir had some type of adverse effect. If all of that is true and the more anemic medicine ends up being used by most doctors thanks to the smear campaign against hydroxychloroquine, the average American will beg to vote from home.


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).


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.


Home Inventions Quotations Game Design Atari Memories Personal Pages About Site Map Contact Privacy Policy Tip Jar