Assembly Language Programming

Lesson 6: Binary Logic

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

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Page Table of Contents

Original Lesson

I know I promised to start discussing State Machines in Lesson 6, but now I see that I forgot to talk about binary logical functions. Since I just covered binary counting, and binary math; I think it would be best to push State Machines off to lesson 7 and cover binary logic now.






What is logic? I could spend days on that topic, so I need to focus on logic as it applied to programming computers. Recall our discussion of bits in Lesson 2. Each bit has one of two possible values 0 or 1. As the programmer you can apply any meaning you wish to each bit your program uses. A common use for bits is to indicate TRUE or FALSE. TRUE is usually represented by 1, and FALSE is represented by 0. Such an arrangement is called positive logic. You can also use negative logic, where TRUE is 0 and FALSE is 1. For this lesson I will confine the discussion to positive logic for all of the examples, since the instructions in the 650X microprocessors use positive logic.


For this class we are interested in logic functions that we can perform between pairs of bits representing TRUE and FALSE. Some interesting things can be done with bits using just a few simple logical rules.






Logic Functions

There are four basic logical functions: AND, OR, XOR, NOT. You can also combine NOT with the other 3 to form 3 more functions: NAND, NOR, and XNOR. I will discuss each logical function in detail.


Note: For all the experienced programmers reviewing this material, I decided to exclude the logical bit-shift operations from this lesson. I will cover bit-shifting and rotations when I cover those instructions.


The best way to think about binary logical functions is as a special math operator akin to adding and subtracting as we covered in the previous lesson. For all the logical operations, except NOT, there are 2 arguments and a single result. So like addition we can write logical operations as A (oper) B = C, where (oper) is the symbol of the logical function to be performed on A and B resulting in C.





Logical AND

The first function I will present is AND. The function AND is easy to understand. Given A and B, C is TRUE only if A and B are TRUE. Otherwise, C is FALSE. We can present the AND function as a truth table:

   A       B       | C

   -----   -----   | -----




   TRUE    TRUE    | TRUE

As a programmer you will use AND to determine if multiple conditions are TRUE at the same time.


For example:


  A = TRUE if the player is carrying the Blue Key.

  B = TRUE if the player is touching the Blue Door.

  C = TRUE if the player has the Blue key and is touching the blue door.

  If C is TRUE, then unlock the Blue Door and play sound effect.

Note: Above, is an example of what is called pseudocode. Its a list of instructions similar to what an actual program section will look like, but it is written in English rather than the programming language. I will be using psuedocode more and more in these lessons, and you need to get comfortable both reading and writing pseudo code as part of this class. Expect to see exercises where you will read and write pseudocode.


The symbol for AND is &. So, C = A AND B = A & B is the same thing.





Logical OR

The next logical function is OR. Given A and B, C is TRUE if either A or B is TRUE, or both A and B are TRUE. Logical OR in an 'inclusive-OR', not an 'exclusive-OR' as represented by the XOR function to be discussed next. Here is the truth table for OR:

   A       B       | C

   -----   -----   | -----


   FALSE   TRUE    | TRUE 


   TRUE    TRUE    | TRUE

The shorthand symbol for OR is '|'. So, C = A OR B = A | B, is equivalent.





Logical XOR

XOR stands for exclusive OR. C is TRUE if either A or B is TRUE, but it is FALSE if A and B are both TRUE or both FALSE. Here is the truth table for XOR:

   A       B       | C

   -----   -----   | -----


   FALSE   TRUE    | TRUE 


   TRUE    TRUE    | FALSE

The shorthand symbol for XOR is '^'. So, C = A XOR B = A ^ B is equivalent.





Logical NOT

The function NOT is special in that it takes only 1 argument, not 2. It is akin to using the negative sign in arithmetic to make a number negative. C is the opposite state of the input A. So C is FALSE if A is TRUE. C is TRUE if A is FALSE. Here is the truth table for NOT:

   A       | C

   -----   | -----


   TRUE    | FALSE

A common way to represent the function NOT is to place a bar over the input like this:


   A = NOT A

Another way is to use a tilde like this:

   ~A = NOT A

The second method is easier to implement in the ASCII text of this lesson, but the first method is easier to read (I think). I will try to use the bar notation in my lessons, but if it gets too annoying to type, I may start using the tilde.






The functions NAND, NOR, and XNOR are the logical opposites of AND, OR, and XOR. Its shorthand:


  A NOR B = NOT (A OR B)


Here are the truth tables for NAND, NOR, and XNOR:


   A       B       | C

   -----   -----   | -----


   FALSE   TRUE    | TRUE 


   TRUE    TRUE    | FALSE


   A       B       | C

   -----   -----   | -----




   TRUE    TRUE    | FALSE


   A       B       | C

   -----   -----   | -----




   TRUE    TRUE    | TRUE

For notation, I will simply use the NOT bar or tilde in combination with the exiting notation for AND, OR, or XOR.


   A NAND B = NOT (A AND B) = A & B = ~(A & B)


   A NOR B = NOT (A OR B) = A | B = ~(A | B)


   A XNOR B = NOT (A XOR B) = A ^ B = ~(A ^ B)





From Bits to Bytes

I described the functions above in terms of pairs of bits resulting in a single bit. In programming 650X assembly language, you will perform these functions on pairs of bytes. For each input byte you perform the logic function between the corresponding pairs of bits from each input byte, and place the result bit in the corresponding position in the result byte. Look at the graphic examples below for a picture of the operation.





Some Practical Logic

As an assembly language programmer you will make frequent use of binary logic functions in your programs. In this section I provide some practical examples for AND, OR, and XOR. As a programmer you will often use individual bits within bytes to indicate whether conditions in your game environment are TRUE or FALSE, such bits are often referred to as flags. You will often group flags together into bytes to save space in the limited memory of your computer. You will use the AND, OR, XOR logical functions to clear, set, and toggle those flags as events happen in your game.






The function AND is often used in programs to reset one or more bits in a byte to zero, while leaving the other bits unchanged.




Given: %11011010


Say you want to be sure that the MSB and LSB of the given byte are clear. In this example the LSB is already clear, but you don't want to waste time in your code to figure out if the bits are set and then clear them. With AND you can just clear them.


The first step is to create the necessary bit-mask. The bit mask is a byte value that will preserve the bits you want unchanged and clear the bits you want cleared. For each bit to be cleared, reset the bit in the bit mask to 0. For each bit in the given byte to be unchanged, set the bit in the bit mask to 1. So to clear the MSB and LSB, but preserve all other bits as is.


Bit mask is: %01111110

   C = Given & bitmask = %11011010 & %01111110 = %01011010


           %11011010                              ||||||||

         & %01111110                              ||||||||

         -----------                              ||||||||

            ||||||||                              ||||||||

            |||||||+--> 0 & 0 = 0 ----------------++++++++

            ||||||+---> 1 & 1 = 1 ----------------+++++++

            |||||+----> 0 & 1 = 0 ----------------++++++

            ||||+-----> 1 & 1 = 1 ----------------+++++

            |||+------> 1 & 1 = 1 ----------------++++

            ||+-------> 0 & 1 = 0 ----------------+++

            |+--------> 1 & 1 = 1 ----------------++

            +---------> 1 & 0 = 0 ----------------+






The OR function is often used to set individual bits to 1 within a byte without changing the state of other bits in the byte. As with using AND to clear bits in a byte, we don't care if the bits are already set will be set by OR'ing the byte with a corresponding bit mask. Every bit we want set in the byte must be set in the bit mask. Any bit clear in the bit mask will be unchanged after the OR.




Given: %11011010 - use OR to set the MSB and LSB.


Bit mask = %10000001

   C = Given | bitmask = %11011010 | %10000001 = %11011011


           %11011010                              ||||||||

        or %01111110                              ||||||||

           ---------                              ||||||||

            ||||||||                              ||||||||

            |||||||+--> 0 | 1 = 1 ----------------++++++++

            ||||||+---> 1 | 0 = 1 ----------------+++++++

            |||||+----> 0 | 0 = 0 ----------------++++++

            ||||+-----> 1 | 0 = 1 ----------------+++++

            |||+------> 1 | 0 = 1 ----------------++++

            ||+-------> 0 | 0 = 0 ----------------+++

            |+--------> 1 | 0 = 1 ----------------++

            +---------> 1 | 1 = 1 ----------------+






The XOR function is often used in code to flip/toggle the state of specific bits in a byte without effecting other bits in the byte. If the bit is 1 it is flipped to 0. If the bit is 0 it is flipped/toggled to 1. As with AND to clear bits, and OR to set bits, for XOR you must create a bitmask to indicate which bits are to be toggled and which are to be unchanged. Each bit set in the bitmask will toggle the bit in the target byte. Each bit in the bitmask reset to 0 will be unchanged in the target byte.




Given: %11011010 - use XOR to toggle the MSB and LSB.


Bit mask = %10000001

   C = Given ^ bitmask = %11011010 ^ %10000001 = %01011011


           %11011010                              ||||||||

        or %01111110                              ||||||||

           ---------                              ||||||||

            ||||||||                              ||||||||

            |||||||+--> 0 ^ 1 = 1 ----------------++++++++

            ||||||+---> 1 ^ 0 = 1 ----------------+++++++

            |||||+----> 0 ^ 0 = 0 ----------------++++++

            ||||+-----> 1 ^ 0 = 1 ----------------+++++

            |||+------> 1 ^ 0 = 1 ----------------++++

            ||+-------> 0 ^ 0 = 0 ----------------+++

            |+--------> 1 ^ 0 = 1 ----------------++

            +---------> 1 ^ 1 = 0 ----------------+





More Logic

There is much more to binary logic, often called Boolean math after its inventor. This lesson has covered enough for our needs, but there is plenty more information and advanced techniques for simplifying complex logical equations, for example:


   E = ((A & B) | (C ^ D ))  & A

We aren't interested in such complex logic in a beginners course, but feel free to explore the topic yourself if interested. Search the Internet for "Boolean Math".







1.Given the following bytes (A) and bitmask (B) values calculate the result C, for C = A & B, C = A | B, and C = A ^ B.

  1. A = %11111111, B=%10101010
  2. A = %00000000, B=%01010101
  3. A = %11110000, B=%01110111


2.Given the following bytes (A) and bitmask (B) values calculate the result C, for C = A NAND B, C = A NOR B, and C = A XNOR B.

  1. A = %10110110, B=%00000000
  2. A = %11111111, B=%11111111


3.Fill in the blanks '_____' in this pseudocode example with what you believe is the correct logical function.


SUBROUTINE CheckPlayerStatus


        IF (PLAYER.has_key = TRUE) ___ (Player.is_touching_door) THEN

  Goto PlayerExitsLevel

        ELSE IF (Player.touching_monster = TRUE) ___ (Player.touching_arrow) THEN

  Goto PlayerKilled 

  ELSE IF (Player.touching_gold = TRUE) ___ (Monster.died) THEN

  Goto PlayerGetsPoints


END CheckPlayerStatus

4.Bonus Puzzler!!!!
You are running low on available memory for your game. You need to store 2 different counters of events occurring in your game. The first counter counts up from 0 to 7, when the counter reaches 7 the next time it is added to it resets to zero. The second counter, will count down from 13 to 0, once the counter is at zero it stays at zero even if it is decremented again. Devise a method for using binary addition and subtraction in combination with AND, OR, or NOR logic functions to allow you to store both counters in a single byte. You must be able to change either counter without affecting the other. Write the pseudo code to change each counter without affecting the other. Your solution must not share any bits between the two counters even though such a solution is technically possible, you do not have enough free clock cycles left in your program to use such a technique.







Answers provided by Thomas Jentzsch.

1.Given the following bytes (A) and bitmask (B) values calculate the result C, for C = A & B, C = A | B, and C = A ^ B.

a.A = %11111111, B=%10101010

    %10101010, %11111111, %01010101 


b.A = %00000000, B=%01010101

     %00000000, %01010101, %01010101


c.A = %11110000, B=%01110111

     %01110000, %11110111, %10000111



2.Given the following bytes (A) and bitmask (B) values calculate the result C, for C = A NAND B, C = A NOR B, and C = A XNOR B.

a.A = %10110110, B=%00000000

    %11111111, %01001001, %01001001


b.A = %11111111, B=%11111111

    %00000000, %00000000, %11111111



3.Fill in the blanks '_____' in the pseudocode example with what you believe is the correct logical function.

    AND, OR, OR




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 Six Instruction Groups

The 6502 Instruction Set broken down into 6 groups.

6502 Instruction Set

Nice, simple instruction set in little boxes (not made out of ticky-tacky).



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

An easy-to-read 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 6502-related information in the world.

NMOS 6502 Opcodes

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.

Instruction Set

Gives a summary of whole instruction set.

Addressing Modes

Describes each of the 6502 memory addressing modes.

Instruction Reference

Describes the complete instruction set in detail.



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. Stella finally got Atari 2600 quality sound in December of 2018. Until version 6.0, the game sounds in Stella were mostly OK, but not great. Now it's almost impossible to tell the difference between the sound effects in Stella and a real Atari 2600.




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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Negative Ions = Good

Negative ions are good for us. You might want to avoid positive ion generators and ozone generators. 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.



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Watch these two videos for more information:

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How to Wake Up Normies

Charlie Robinson had some good advice about waking up normies (see the link to the video below). He said instead of verbally unloading or being nasty or acting like a bully, ask the person a question. Being nice and asking a question will help the person actually think about the subject.


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