By Robert M (adapted by Duane Alan Hahn, a.k.a. Random Terrain)
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Page Table of Contents
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.
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.
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 ----- ----- | ----- FALSE FALSE | FALSE FALSE TRUE | FALSE TRUE FALSE | FALSE TRUE TRUE | TRUE
As a programmer you will use AND to determine if multiple conditions are TRUE at the same time.
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.
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 FALSE | FALSE FALSE TRUE | TRUE TRUE FALSE | TRUE TRUE TRUE | TRUE
The shorthand symbol for OR is '|'. So, C = A OR B = A | B, is equivalent.
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 FALSE | FALSE FALSE TRUE | TRUE TRUE FALSE | TRUE TRUE TRUE | FALSE
The shorthand symbol for XOR is '^'. So, C = A XOR B = A ^ B is equivalent.
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 ----- | ----- FALSE | TRUE 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 NAND B = NOT (A AND B) A NOR B = NOT (A OR B) A XNOR B = NOT (A XOR B)
Here are the truth tables for NAND, NOR, and XNOR:
NAND: A B | C ----- ----- | ----- FALSE FALSE | TRUE FALSE TRUE | TRUE TRUE FALSE | TRUE TRUE TRUE | FALSE NOR: A B | C ----- ----- | ----- FALSE FALSE | TRUE FALSE TRUE | FALSE TRUE FALSE | FALSE TRUE TRUE | FALSE XNOR: A B | C ----- ----- | ----- FALSE FALSE | TRUE FALSE TRUE | FALSE TRUE FALSE | FALSE 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)
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.
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.
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 ----------------+
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".
SUBROUTINE CheckPlayerStatus BEGIN IF (PLAYER.has_green_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 ENDIF END CheckPlayerStatus
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Other Assembly Language Tutorials
Lesson 6: Binary Logic
This book was written in English, not computerese. It's written for Atari users, not for professional programmers (though they might find it useful).
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 6502 Instruction Set broken down into 6 groups.
Nice, simple instruction set in little boxes (not made out of ticky-tacky).
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 easy-to-read page from The Second Book Of Machine Language.
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.
By John Pickens. Updated by Bruce Clark.
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.
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.
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.
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).
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.
Adapted information and charts related to Atari 2600 music and sound.
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.
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.
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.
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.
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 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 surroundair.com. 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.
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.
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:
Hydrofracking is bad for you, your family, your friends, and the environment.
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 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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