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PT3P1\TXT
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
Tape/disk: | Home » Personal collection » Acorn ADFS disks » Greaseweazled » adfs_IJJOBS21.adf |
Filename: | PT3P1\TXT |
Read OK: | ✔ |
File size: | 6CDD bytes |
Load address: | FFFFFF48 |
Exec address: | 4EA3B268 |
Duplicates
There are 2 duplicate copies of this file in the archive:
- Personal collection » Acorn ADFS disks » Archimedes » IJJOBS21.ADF » PT3P1\TXT
- Personal collection » Acorn ADFS disks » Greaseweazled » adfs_IJJOBS21.adf » PT3P1\TXT
- Personal collection » Acorn hard disk » misc » dcfprogs » PT3P1.TXT
File contents
Programming Technique Part 3: Graphics - Screen Memory Written by Dominic Ford At the end of the last article, you could program graphics in colour using the built in MOVE and DRAW commands in BASIC, and could program fast, detailed graphics in black and white using user defined characters. But there was a problem if we wanted graphics in both colour and detail, as by both methods the production of such graphics would be incredibly slow. There is a solution to this problem, which involves taking advantage of the way in which the computer's video system operates. The colour of each pixel on your monitor is determined the data sent to the monitor by your computer - thats fairly obvious. But if you have drawn a very complex set of shapes on the computer screen, perhaps using a BASIC program which took several hours to calculate and draw the result you see on the screen, how does the computer remember the colour of every pixel on the screen, and know what data to send to your monitor? The answer is simple: within your computer's memory there is an area set aside to store the colour of every pixel on the screen, and when the monitor requests the colour of a particular pixel, the computer simply reads the colour of the pixel from this area of memory. This area of memory is called "Screen Memory". It can be considered as a sort of giant table, holding data for the colours of all of the pixels in a huge matrix of memory locations. But of what use is this to the programmer you might be wondering. The answer is that when you use user defined characters, MOVE and DRAW commands, or any other method of putting anything on the screen, the computer simply alters a few values in this giant table. But the computer takes time to process your MOVE and DRAW commands to work out which values in the table to alter. If you could bypass this stage, and set the values in this giant table yourself without using the computer's general purpose graphics commands, you can get exactly the result that you want, and much faster than you would achieve if you were doing the operation through the computer's commands. These have to process the parameters which you give, and then calculate where abouts in the giant table you want to alter, before they can actually do any useful work. Thus a lot of computer time is wasted in performing calculations, which can actually be skipped if the programmer is careful. There are two possible ways of achieving this idea, both of which are useful in different situations: 1. Save screen memory to disc. This idea is fairly simple to understand. You, as the programmer, write a program to plot the artwork for your program onto the screen, taking however many hours it may take to complete all of the calculations required to plot the graphics. You run this program once on your computer, so that your masterpiece is stored in the screen memory of your computer (ie. is on the monitor of your computer). You than transfer the entire contents of the screen memory on your computer to floppy disc. Then, in the final program which you want the user to operate, you include a command to load this data back from floppy disc into the screen memory of their computer. In a matter of a couple of seconds, graphics which took possible hours to calculate will appear on their screen. This is a technique which I have used in several of my programs. The main menu of Shipwrecked II: Jupiter 3, where you select Play, Instructions, Game Complete or Cheat with the starfield backdrop was done in this way - the screen took nearly an hour for my computer to calculate, but I was able to make it appear in seconds on your screen. I should also mention the title screen to Shipwreck with the animated sea, not to mention the endless EUG title screens I have done in this way - the Christmas EUG 35 screen with the swirly blue background (credited erroneously to Robert Sprowson) took two whole days to plot! In order to achieve this, you simply need to understand two BASIC commands: *SAVE Filename nnnn mmmm *LOAD Filename nnnn These load and save areas of the computer's memory to floppy disc or cassette with the filename givan in place of the work Filename, starting at memory location nnnn, and continuing until memory location mmmm (where nnnn and mmmm are both in hexidecimal - base 16). Don't worry if you don't entirely understand this - it is not necessary to entirely understand the workings of these commands, or of hexidecimal to use them to store and retrieve screen memory. All you need to do is substitute nnnn and mmmm for the addresses of the start and finish of screen memory. The location of these within your computer varies depeding upon which graphics mode you are using (which you selected using the MODE command - see previous tutorial if you are unsure of what this is), but is always constant for any particular mode. the values for the different modes are given below: Mode nnnn mmmm NOTES: 0 3000 7FFF 1 3000 7FFF - nnnn and mmmm values given to the left are 2 3000 7FFF all in hexidecimal. Therefore they can be 3 4000 7FFF substituted directly into the *LOAD and *SAVE 4 5800 7FFF commands with no conversion required. 5 5800 7FFF 6 6000 7FFF - Values are not valid for the BBC model A in 7 7C00 7FFF modes 4,5,6 or 7. Examples: Suppose you are in mode 2, and want to store the screen to a floppy. From the table above, nnnn is 3000 and mmmm is 7FFF for mode 2. Therefore, to save the screen under the filename "Screen", you would type: *SAVE Screen 3000 7FFF Now, if you want to restore the screen again, and put your graphics back on the screen again, you would use *LOAD. Notice that this time only a value for nnnn is required, and not for mmmm: *LOAD Screen 3000 You can try this out now, if you switch on your Electron, and insert a work disc into your floppy drive. If you use ADFS, you may need to use *MOUNT to select the floppy disc, and be able to write to it. Now enter mode 2 by typing: MODE 2 Now type some text on the screen which will represent the graphics which you want to save. When you have finished, save the contents of screen memory to floppy disk as shown above, by typing: *SAVE Screen 3000 7FFF When the disk drive has finished, clear the text off the screen by typing: CLS The text which you typed onto the screen has now been wiped from the computer's memory, but should still be stored on the floppy disc. We can show that this is so by typing: *LOAD Screen 3000 Your text should now reappear on the screen. You can repeat this with any kind of complex graphics on screen, and it will still work. The same can be done in any other graphics mode, simply by changing the values of nnnn and mmmm to those given in the table above. For example in mode 5 you would use: *SAVE Screen 5800 7FFF followed by: *LOAD Screen 5800 7FFF There are, however, a few precautionary points which should be mentioned about this technique of saving screen memory: - As you probably realise, in four colour modes, the four colours you can use can be changed from the default black, red, yellow and white by using VDU 19 to change the palette. The colours in the palette are not saved when this technique is used, and must be restored by repeating the VDU 19 commands again. If you define the palette to, for example, black, blue, cyan and white, and create a picture which looks good in this colour scheme, you must remember that unless you define the palette to these four colours before performing *LOAD to restore the picture, it may appear rather odd when reloaded, as it will appear in black, red, yellow and white - the default colour scheme. - The exact reason why this happens is rather complicated, but if you allow the cursor to go down off the bottom line of the screen, and allow the screen to scroll up one line, this technique stops working until you perform a MODE command, or clear the screen using CLS. Basically what happens is that the computer does not physically move every line of text on the screen up one line, but instead makes a note that every line in screen memory is stored one line lower than it should be. When you reload from disk, this note is lost, and the computer draws every line lower than it should be. Each time that CLS or MODE is executed, screen memory is cleared and reinitiated, so that every line is stored in memory where you would expect it to be. Simply remember not to allow the screen to scroll between clearing it, and saving the contents of screen memory to disc. - The files created when you save the contents of screen memory to disk are fairly large - so large, in fact, that you can often only fit around 15 such files onto each disk that you use (the exact number depends upon what modes the images are in). Therefore this technique is not feasable for a large number of images. Each screen in a game like Shipwrecked cannot be stored in this way - if I had stored every screen of the game like this, it would have required six floppy disks to store the data for the game! This means that saved screens must be reserved for the purposes of title screens only. Earlier in the article, I mentioned several examples of screens which I have done for EUG using saved screens using this technique. These included the title screens for both Shipwrecked games, and also several EUG title screens. You may have noticed that these were actually animated (see the starfield in Jupiter 3 and the EUG 35 title). This was achieved by palette switching as used in the previous article. If you look again at the programming technique demonstration from this article (on EUG 36), and select option 5, the same effect will appear on your screen. The same principal was applied in both animated screens mentioned above - the only difference is that in these title screens the pattern on screen which is being palette switched is rather more complex. Shipwreck's title screen (with the animated water scene) was also created in this way, except that for this screen there was also a machine code program altering the contents of screen memory as well, to enhance the effect. So, we have a technique which allows us to store a small number of very detailed screens on floppy, and recall then at very great speed. But what if we want to use this method for a large number of screens? And what if we want a situation like a game, where the user can move sprites on the screen around. This can also be done by altering the values in screen memory directly, but in a different way... 2. Editing screen memory The basic idea is this: in any program, you only usually require a certain, small number of little 'blocks' to make up a whole picture. In a word processor, for example, you only need the letters of the alphabet to appear on the screen. These letters are small blocks of graphics which appear on your screen (called characters). Because only these 26 blocks are required, the word processor does not need to store every letter as all of the pixels which make it up (ie. as a bitmap), but just as a code for that particular letter. When the word processor wants to display a letter on the screen, it looks up the letter code, and then copies the graphic data for what that letter looks like onto the screen. Therefore, the graphic data for what colour all of the pixels should be for that particular letter (which might take several bytes) need only be stored once, and that letter can be stored in your script in just one byte, for the letter code. Thus, the memory taken up by your script is reduced dramatically. The same principal can be used in graphics. Look at two brick walls in an arcade adventure such as Shipwrecked - can you see the difference between them? If they are the same, surely you only need to store the graphic data for a brick wall once, and then copy it onto the screen whenever you want a brick wall. In Shipwrecked, for example, the graphic data to describe what a brick wall looks like took 128 bytes. Yet every time I wanted that brick wall (which was over a hundred times) I could simply use one byte to say "Put a brick wall here!". The easiest way to use this block idea, as you may already have realised, is using user defined characters. You redefine the letters of the alphabet as different pictures, and then use the standard BASIC PRINT command to output these pictures to the screen, as and when they are required. But, as we already realised in the last article, this only allows you to use one colour in each character. Even so, this is a reasonable technique if you don't mind the lack of colour. Many commercial games actually never addressed this problem, and had graphics which lacked colour somewhat. Even Dizzy (for those who have never heard of it, a great arcade adventure of the 1980s, which caused quite a cult following at the time on the Spectrum and C64, but never quite reached the Elk) did not have more than one colour (other than black) per block. Different blocks were, however, different colours - trees were green and the ground was red - but there was never any overlap between the two colour areas. There is, however, a way of creating an effect just like user defined characters, but in full colour, and the principal is very similar to that used before in saving screen memory. Basically, you design you small block on the screen, using whatever technique you like to draw it, and then save the small part of screen memory which contains your design. This time, however, you will not save it to floppy disc, but to another area of memory. You can then copy this block back to screen memory whenever and wherever you want it. If you want it, say, in the fifth row down, and twelve characters along, you can calculate where abouts this corresponds to in screen memory, and copy the block to this location. As the block is stored in your computer's RAM, as opposed to on floppy, this transfer can be done by machine code at very great speed (taking only a small fraction of a second). For those programmers who are not familiar with machine code, a module is included with this tutorial allowing you to do this. The program code for this module is actually taken directly from Shipwrecked. If you are not familiar with machine code, then you can probably skip the next section on how to directly access screen memory, as it is impossible to achieve any speed by accessing screen memory directly in BASIC - your program will crawl along incredibly slowly. You could still use such a technique in preparing a screen which you intend to save to floppy using the technique described before with *SAVE and *LOAD. Firstly, it is important to know how screen memory is laid out in memory. The exact position of each character within the memory of your computer varies from one graphics mode to another, but the basic principals are the same: - The screen area is divided up into characters. These are blocks of eight pixels by eight pixels, and are the same size as the rectangular block of space taken up by one letter when you print text to the screen. Screen memory is divided up into blocks, with each the characters being defined by one of these blocks. - The screen is stored row by row, with the top row first and the bottom row last. - Within each of these rows, characters are stored one by one, from left to right. - In all modes, screen memory ends at &7FFF (ie. at the end of RAM) Footnote: By convention, memory addresses are specified in hexidecimal. I use the standard Acorn '&' prefix to indicate hexidecimal values. Those used to dealing with PCs are any other computers may be used to the American convention of using a dollar prefix in its place. It should be noted that the Elk expects & and will not accept $. Example: Suppose I want to draw a blob in character square (6,7), in mode 1. What is the address of this square? (given that each character takes 16 bytes of screen memory to define in mode 1 - we'll come to how to calculate this in a minute). Well - looking at the table earlier, screen memory starts at &3000 in mode 1. We want to find the start of row 7 in screen memory. This row has 7 rows of characters above it, and which will be stored before it. Each of these rows consists of 40 characters, which take up 16 bytes each. Therefore the total memory taken up by these rows is 7 * 40 * 16 = 4480 bytes. [Each character is 16 bytes, each row consists of 40 of these characters, therefore we multiply by 40, and as there are 7 of these complete rows, we multiply by 7 to get the value for seven of these rows] Now we have that the starting address of row 7 is at: &3000 + 4480 = &4180 Now that we have found where abouts in memory this row starts, we need to locate character 6. This should be fairly easy - we know that characters are stored from left to right, so just add on the memory required to store six characters to the left of the one we want, i.e. 16 * 6 = 96 bytes [Six characters, each taking 16 bytes to store]. Therefore the address of character (6,7) will be: &4180 + 96 = &41E0 Answer: Character (6,7) is stored from &41E0 to &41EF Just to check the answer is correct, type this simple loop: 10 MODE 1 20 FOR ad=&41E0 TO &41EF 30 ?ad=255 40 NEXT And yes, a white splodge does appear in square (6,7). This whole procedure can actually be refined down, and expressed as a simple formula: Address = Base + ( y * No. characters per line + x ) * Memory per character Where: Address= The memory location of the start of the character you want. Base = Start of screen memory in current graphics mode. (x,y) = Co-ordinate of square you want to access (same as PRINT TAB) Since the number of characters per line, the number of bytes per character, and the base address of screen memory are all constant for any particular graphics mode, the values for the graphics mode you are using can be substituted into the equation in your program. For mode 1, for example, you would use: Address = &3000 + (40 * y + x) * 16 Before continuing, one note should be borne in mind. You may remember that a while back I mentioned that when you type text which overflows off the bottom of the screen, the computer makes a note that each line is stored in memory one line lower than it should be, but does not actually move anything around in screen memory. The same effect can cause problems with direct access to screen memory as well. The simple rule for beginners is, NEVER attempt to use direct screen memory access when there is even the slightest possibility that the screen might have been allowed to scroll up at all (e.g. after using INPUT to get input from the user - how do you know that they didn't type so much that it went of the bottom of the screen?) If you know what you are doing, this rule can be ignored, and high-speed scrolling can be achieved as a result, but that is not for the beginner! I can tell you from first hand experience, that creating scrolling in Jupiter 3 by this technique was a nightmare - especially when the operating system calls you need to make to achieve this are completely different on the BBC to the Elk, so you need to find out which platform you are operating on, and then make the relavant calls for that platform! Now that you can locate a the memory occupied by a character in screen memory, you need to know how the bytes within this block are laid out, so that you can have pixel by pixel control over your monitor screen. This is also required if you are to be able to calculate the amount of memory taken up by each character's definition in a particular mode. The graphics modes can be divided into three categories: monochrome modes (ie. two colours), four colour modes, and sixteen colour modes. All of the Elk's modes fall into these three groupings. Which of these colours each pixel of the screen is depends upon the status of a number of binary bits. These have two states, 0 or 1. Now, in a monochrome mode, one bit is sufficient to define the colour of one pixel (bits have two states, 0 or 1, and the pixels have two states, colour 0 or colour 1). In a four colour mode, on the other hand, one bit will not be sufficient, as four different states are required. Two bits will be enough to store the colour of one pixel, however: Bit 1 state Bit 2 state Colour 0 0 0 0 1 1 1 0 2 1 1 3 Those familiar with binary will spot the pattern straight away - simply convert the binary value of the two bits into decimal, and you have the logical colour number. A very similar pattern applies to MODE 2 - the Elk's 16 colour mode. Each pixel requires 4 bits to store its colour (2^4=16). Once again, the colour of the pixel is the logical colour whose number is given when the four bits are put together to form a binary value: Bit 1 state Bit 2 state Bit 3 state Bit 4 state Colour Default 0 0 0 0 0 BLK 0 0 0 1 1 RED 0 0 1 0 2 GRN 0 0 1 1 3 YEL 0 1 0 0 4 BLE 0 1 0 1 5 MGT 0 1 1 0 6 CYN 0 1 1 1 7 WHT 1 0 0 0 8 BLK/WHT 1 0 0 1 9 RED/CYN 1 0 1 0 10 GRN/MGT 1 0 1 1 11 YEL/BLE 1 1 0 0 12 BLE/YEL 1 1 0 1 13 MGT/GRN 1 1 1 0 14 CYN/RED 1 1 1 1 15 WHT/BLK [Default: Default setting of this logical colour when MODE 2 is first entered] So... the Electron has modes where the definition of the colour of a certain pixel can take 1, 2 or 4 bits. As each byte of the electron's memory consists of 8 seperate bits, this means that in monochrome modes we can fit 8 pixels into each byte (8/1=8). In four colour modes (where each pixel requires two bits) we can fit 4 pixels into each byte (8/2=4). Finally in MODE 2 (the sixteen colour mode where each pixel requires 4 bits) we can fit two pixels into each byte. Let's now look at how each is laid out in more depth: MONOCHROME MODES: These are laid out in the simplest way, as eight pixels fit into each byte. The character, remember, consists of an 8 by 8 square of pixels. The data is stored in the same way as user defined characters are defined using VDU23. The first byte of the definition defines the top row of eight pixels; the second defines the second row down, etc. Thus the entire character can be defined in eight bytes, and this is the number of bytes of the Elk's memory which is used by each character. Note - the most significant bit of each byte defines the left-most pixel of the row, and the least significant bit defines the right-most pixel (just as with VDU 23 definitions) FOUR COLOUR MODES: This time each byte can only hold four pixels. Once again, each byte holds a number of pixels which are in a horizontal line. This time, as before, the first eight bytes run down in a vertical line. This time, though, not all of the pixels in the character are being defined, and only the left most 4 pixels. The right-most four pixels are defined in a second downward vertical sweep. Thus the total memory allocation for each character is sixteen bytes. The layout is shown more clearly using a diagram. This shows the eight by eight block of pixels in a character, and each has the offset of the memory location where this pixel is stored from the start of the character definition. Offsets are given in hexidecimal: PIXEL-BY PIXEL LAYOUT MEMORY FLOW 00008888 0 8 11119999 � � 2222AAAA � � 3333BBBB � � 4444CCCC � � 5555DDDD � � 6666EEEE \ / \ / 7777FFFF 7 F Each of these sixteen bytes, as already discussed, contains four pixel definitions. But within the byte's eight bits, they are not laid out as you might at first imagine. If we call the four pixels A, B, C and D (A is left-most, D is right-most), the lay out is: [MOST SIGNIFICANT] A1 B1 C1 D1 A0 B0 C0 D0 [LEAST SIGNIFICANT] Where: A1: Most significant bit of A's definition � Two bit definition A0: Least significant bit of A's definition � of pixel A. The same pattern holds for B, C and D. Example: Let's suppose we want to set the colour of the left-most pixel in a byte of a four colour mode to be colour 3. We would use: ?address=(?address AND &77) OR &88 Explanation - The (?address AND &77) bit clears the two bits defining the pixel that we want to change. The OR &88 then sets the two bits that we want set. This way we ensure that when we are going way from colour 1 to colour 2, the least significant bit of the definition is cleared as well as the most significant bit being set. It is important to notice the pattern in these bits - each pixel requires a two bit definition, but these two bits are not next to each other in the byte - instead all of the high-bytes are stored together, and all of the low-bytes are stored together. SIXTEEN COLOUR MODES The pattern for sixteen colour modes is similar to that found in four colour modes, except that each byte can only store two pixels (each occupies four bits). As with previous cases, the pixels are stored in a number of vertical sweeps starting at the left of the character, and moving to the right. This time, though, four vertical sweeps are required to cover the entire character, not two as with four colour modes: PIXEL-BY PIXEL LAYOUT MEMORY FLOW 00880088 0 8 10 18 11991199 � � � � 22AA22AA � � � � 33BB33BB � � � � 44CC44CC � � � � 55DD55DD � � � � 66EE66EE \ / \ / \ / \ / 77FF77FF 7 F 17 1F NB: Offsets given in hexadecimal. Values in right half of left diagram should have &10 added to them (only least significant character given) The pattern of the layout of the pixel data in each of the bytes is also similar to that for the four colour modes (the two pixels are A and B, and each comprises of four bits 0-3, where 0 is least significant and 3 is most significant). [MOST SIGNIFICANT] A3 B3 A2 B2 A1 B1 A0 B0 [LEAST SIGNIFICANT] Notice that once again bits defining the pixels A and B are not stored together, but those defining the least/most significant bits are stored together.
00000000 50 72 6f 67 72 61 6d 6d 69 6e 67 20 54 65 63 68 |Programming Tech| 00000010 6e 69 71 75 65 0d 0a 50 61 72 74 20 33 3a 20 47 |nique..Part 3: G| 00000020 72 61 70 68 69 63 73 20 2d 20 53 63 72 65 65 6e |raphics - Screen| 00000030 20 4d 65 6d 6f 72 79 0d 0a 0d 0a 57 72 69 74 74 | Memory....Writt| 00000040 65 6e 20 62 79 20 44 6f 6d 69 6e 69 63 20 46 6f |en by Dominic Fo| 00000050 72 64 0d 0a 0d 0a 41 74 20 74 68 65 20 65 6e 64 |rd....At the end| 00000060 20 6f 66 20 74 68 65 20 6c 61 73 74 20 61 72 74 | of the last art| 00000070 69 63 6c 65 2c 20 79 6f 75 20 63 6f 75 6c 64 20 |icle, you could | 00000080 70 72 6f 67 72 61 6d 20 67 72 61 70 68 69 63 73 |program graphics| 00000090 20 69 6e 20 63 6f 6c 6f 75 72 20 75 73 69 6e 67 | in colour using| 000000a0 0d 0a 74 68 65 20 62 75 69 6c 74 20 69 6e 20 4d |..the built in M| 000000b0 4f 56 45 20 61 6e 64 20 44 52 41 57 20 63 6f 6d |OVE and DRAW com| 000000c0 6d 61 6e 64 73 20 69 6e 20 42 41 53 49 43 2c 20 |mands in BASIC, | 000000d0 61 6e 64 20 63 6f 75 6c 64 20 70 72 6f 67 72 61 |and could progra| 000000e0 6d 20 66 61 73 74 2c 0d 0a 64 65 74 61 69 6c 65 |m fast,..detaile| 000000f0 64 20 67 72 61 70 68 69 63 73 20 69 6e 20 62 6c |d graphics in bl| 00000100 61 63 6b 20 61 6e 64 20 77 68 69 74 65 20 75 73 |ack and white us| 00000110 69 6e 67 20 75 73 65 72 20 64 65 66 69 6e 65 64 |ing user defined| 00000120 20 63 68 61 72 61 63 74 65 72 73 2e 20 42 75 74 | characters. But| 00000130 0d 0a 74 68 65 72 65 20 77 61 73 20 61 20 70 72 |..there was a pr| 00000140 6f 62 6c 65 6d 20 69 66 20 77 65 20 77 61 6e 74 |oblem if we want| 00000150 65 64 20 67 72 61 70 68 69 63 73 20 69 6e 20 62 |ed graphics in b| 00000160 6f 74 68 20 63 6f 6c 6f 75 72 20 61 6e 64 20 64 |oth colour and d| 00000170 65 74 61 69 6c 2c 20 61 73 0d 0a 62 79 20 62 6f |etail, as..by bo| 00000180 74 68 20 6d 65 74 68 6f 64 73 20 74 68 65 20 70 |th methods the p| 00000190 72 6f 64 75 63 74 69 6f 6e 20 6f 66 20 73 75 63 |roduction of suc| 000001a0 68 20 67 72 61 70 68 69 63 73 20 77 6f 75 6c 64 |h graphics would| 000001b0 20 62 65 20 69 6e 63 72 65 64 69 62 6c 79 20 73 | be incredibly s| 000001c0 6c 6f 77 2e 0d 0a 0d 0a 54 68 65 72 65 20 69 73 |low.....There is| 000001d0 20 61 20 73 6f 6c 75 74 69 6f 6e 20 74 6f 20 74 | a solution to t| 000001e0 68 69 73 20 70 72 6f 62 6c 65 6d 2c 20 77 68 69 |his problem, whi| 000001f0 63 68 20 69 6e 76 6f 6c 76 65 73 20 74 61 6b 69 |ch involves taki| 00000200 6e 67 20 61 64 76 61 6e 74 61 67 65 20 6f 66 20 |ng advantage of | 00000210 74 68 65 0d 0a 77 61 79 20 69 6e 20 77 68 69 63 |the..way in whic| 00000220 68 20 74 68 65 20 63 6f 6d 70 75 74 65 72 27 73 |h the computer's| 00000230 20 76 69 64 65 6f 20 73 79 73 74 65 6d 20 6f 70 | video system op| 00000240 65 72 61 74 65 73 2e 20 54 68 65 20 63 6f 6c 6f |erates. The colo| 00000250 75 72 20 6f 66 20 65 61 63 68 20 70 69 78 65 6c |ur of each pixel| 00000260 0d 0a 6f 6e 20 79 6f 75 72 20 6d 6f 6e 69 74 6f |..on your monito| 00000270 72 20 69 73 20 64 65 74 65 72 6d 69 6e 65 64 20 |r is determined | 00000280 74 68 65 20 64 61 74 61 20 73 65 6e 74 20 74 6f |the data sent to| 00000290 20 74 68 65 20 6d 6f 6e 69 74 6f 72 20 62 79 20 | the monitor by | 000002a0 79 6f 75 72 20 63 6f 6d 70 75 74 65 72 20 2d 0d |your computer -.| 000002b0 0a 74 68 61 74 73 20 66 61 69 72 6c 79 20 6f 62 |.thats fairly ob| 000002c0 76 69 6f 75 73 2e 20 42 75 74 20 69 66 20 79 6f |vious. But if yo| 000002d0 75 20 68 61 76 65 20 64 72 61 77 6e 20 61 20 76 |u have drawn a v| 000002e0 65 72 79 20 63 6f 6d 70 6c 65 78 20 73 65 74 20 |ery complex set | 000002f0 6f 66 20 73 68 61 70 65 73 20 6f 6e 0d 0a 74 68 |of shapes on..th| 00000300 65 20 63 6f 6d 70 75 74 65 72 20 73 63 72 65 65 |e computer scree| 00000310 6e 2c 20 70 65 72 68 61 70 73 20 75 73 69 6e 67 |n, perhaps using| 00000320 20 61 20 42 41 53 49 43 20 70 72 6f 67 72 61 6d | a BASIC program| 00000330 20 77 68 69 63 68 20 74 6f 6f 6b 20 73 65 76 65 | which took seve| 00000340 72 61 6c 20 68 6f 75 72 73 0d 0a 74 6f 20 63 61 |ral hours..to ca| 00000350 6c 63 75 6c 61 74 65 20 61 6e 64 20 64 72 61 77 |lculate and draw| 00000360 20 74 68 65 20 72 65 73 75 6c 74 20 79 6f 75 20 | the result you | 00000370 73 65 65 20 6f 6e 20 74 68 65 20 73 63 72 65 65 |see on the scree| 00000380 6e 2c 20 68 6f 77 20 64 6f 65 73 20 74 68 65 20 |n, how does the | 00000390 0d 0a 63 6f 6d 70 75 74 65 72 20 72 65 6d 65 6d |..computer remem| 000003a0 62 65 72 20 74 68 65 20 63 6f 6c 6f 75 72 20 6f |ber the colour o| 000003b0 66 20 65 76 65 72 79 20 70 69 78 65 6c 20 6f 6e |f every pixel on| 000003c0 20 74 68 65 20 73 63 72 65 65 6e 2c 20 61 6e 64 | the screen, and| 000003d0 20 6b 6e 6f 77 20 77 68 61 74 0d 0a 64 61 74 61 | know what..data| 000003e0 20 74 6f 20 73 65 6e 64 20 74 6f 20 79 6f 75 72 | to send to your| 000003f0 20 6d 6f 6e 69 74 6f 72 3f 20 54 68 65 20 61 6e | monitor? The an| 00000400 73 77 65 72 20 69 73 20 73 69 6d 70 6c 65 3a 20 |swer is simple: | 00000410 77 69 74 68 69 6e 20 79 6f 75 72 20 63 6f 6d 70 |within your comp| 00000420 75 74 65 72 27 73 0d 0a 6d 65 6d 6f 72 79 20 74 |uter's..memory t| 00000430 68 65 72 65 20 69 73 20 61 6e 20 61 72 65 61 20 |here is an area | 00000440 73 65 74 20 61 73 69 64 65 20 74 6f 20 73 74 6f |set aside to sto| 00000450 72 65 20 74 68 65 20 63 6f 6c 6f 75 72 20 6f 66 |re the colour of| 00000460 20 65 76 65 72 79 20 70 69 78 65 6c 20 6f 6e 20 | every pixel on | 00000470 74 68 65 0d 0a 73 63 72 65 65 6e 2c 20 61 6e 64 |the..screen, and| 00000480 20 77 68 65 6e 20 74 68 65 20 6d 6f 6e 69 74 6f | when the monito| 00000490 72 20 72 65 71 75 65 73 74 73 20 74 68 65 20 63 |r requests the c| 000004a0 6f 6c 6f 75 72 20 6f 66 20 61 20 70 61 72 74 69 |olour of a parti| 000004b0 63 75 6c 61 72 20 70 69 78 65 6c 2c 20 74 68 65 |cular pixel, the| 000004c0 0d 0a 63 6f 6d 70 75 74 65 72 20 73 69 6d 70 6c |..computer simpl| 000004d0 79 20 72 65 61 64 73 20 74 68 65 20 63 6f 6c 6f |y reads the colo| 000004e0 75 72 20 6f 66 20 74 68 65 20 70 69 78 65 6c 20 |ur of the pixel | 000004f0 66 72 6f 6d 20 74 68 69 73 20 61 72 65 61 20 6f |from this area o| 00000500 66 20 6d 65 6d 6f 72 79 2e 0d 0a 54 68 69 73 20 |f memory...This | 00000510 61 72 65 61 20 6f 66 20 6d 65 6d 6f 72 79 20 69 |area of memory i| 00000520 73 20 63 61 6c 6c 65 64 20 22 53 63 72 65 65 6e |s called "Screen| 00000530 20 4d 65 6d 6f 72 79 22 2e 20 49 74 20 63 61 6e | Memory". It can| 00000540 20 62 65 20 63 6f 6e 73 69 64 65 72 65 64 20 61 | be considered a| 00000550 73 20 61 0d 0a 73 6f 72 74 20 6f 66 20 67 69 61 |s a..sort of gia| 00000560 6e 74 20 74 61 62 6c 65 2c 20 68 6f 6c 64 69 6e |nt table, holdin| 00000570 67 20 64 61 74 61 20 66 6f 72 20 74 68 65 20 63 |g data for the c| 00000580 6f 6c 6f 75 72 73 20 6f 66 20 61 6c 6c 20 6f 66 |olours of all of| 00000590 20 74 68 65 20 70 69 78 65 6c 73 20 69 6e 0d 0a | the pixels in..| 000005a0 61 20 68 75 67 65 20 6d 61 74 72 69 78 20 6f 66 |a huge matrix of| 000005b0 20 6d 65 6d 6f 72 79 20 6c 6f 63 61 74 69 6f 6e | memory location| 000005c0 73 2e 0d 0a 0d 0a 42 75 74 20 6f 66 20 77 68 61 |s.....But of wha| 000005d0 74 20 75 73 65 20 69 73 20 74 68 69 73 20 74 6f |t use is this to| 000005e0 20 74 68 65 20 70 72 6f 67 72 61 6d 6d 65 72 20 | the programmer | 000005f0 79 6f 75 20 6d 69 67 68 74 20 62 65 20 77 6f 6e |you might be won| 00000600 64 65 72 69 6e 67 2e 20 54 68 65 0d 0a 61 6e 73 |dering. The..ans| 00000610 77 65 72 20 69 73 20 74 68 61 74 20 77 68 65 6e |wer is that when| 00000620 20 79 6f 75 20 75 73 65 20 75 73 65 72 20 64 65 | you use user de| 00000630 66 69 6e 65 64 20 63 68 61 72 61 63 74 65 72 73 |fined characters| 00000640 2c 20 4d 4f 56 45 20 61 6e 64 20 44 52 41 57 20 |, MOVE and DRAW | 00000650 63 6f 6d 6d 61 6e 64 73 2c 0d 0a 6f 72 20 61 6e |commands,..or an| 00000660 79 20 6f 74 68 65 72 20 6d 65 74 68 6f 64 20 6f |y other method o| 00000670 66 20 70 75 74 74 69 6e 67 20 61 6e 79 74 68 69 |f putting anythi| 00000680 6e 67 20 6f 6e 20 74 68 65 20 73 63 72 65 65 6e |ng on the screen| 00000690 2c 20 74 68 65 20 63 6f 6d 70 75 74 65 72 20 73 |, the computer s| 000006a0 69 6d 70 6c 79 0d 0a 61 6c 74 65 72 73 20 61 20 |imply..alters a | 000006b0 66 65 77 20 76 61 6c 75 65 73 20 69 6e 20 74 68 |few values in th| 000006c0 69 73 20 67 69 61 6e 74 20 74 61 62 6c 65 2e 20 |is giant table. | 000006d0 42 75 74 20 74 68 65 20 63 6f 6d 70 75 74 65 72 |But the computer| 000006e0 20 74 61 6b 65 73 20 74 69 6d 65 20 74 6f 0d 0a | takes time to..| 000006f0 70 72 6f 63 65 73 73 20 79 6f 75 72 20 4d 4f 56 |process your MOV| 00000700 45 20 61 6e 64 20 44 52 41 57 20 63 6f 6d 6d 61 |E and DRAW comma| 00000710 6e 64 73 20 74 6f 20 77 6f 72 6b 20 6f 75 74 20 |nds to work out | 00000720 77 68 69 63 68 20 76 61 6c 75 65 73 20 69 6e 20 |which values in | 00000730 74 68 65 20 74 61 62 6c 65 0d 0a 74 6f 20 61 6c |the table..to al| 00000740 74 65 72 2e 20 49 66 20 79 6f 75 20 63 6f 75 6c |ter. If you coul| 00000750 64 20 62 79 70 61 73 73 20 74 68 69 73 20 73 74 |d bypass this st| 00000760 61 67 65 2c 20 61 6e 64 20 73 65 74 20 74 68 65 |age, and set the| 00000770 20 76 61 6c 75 65 73 20 69 6e 20 74 68 69 73 20 | values in this | 00000780 67 69 61 6e 74 0d 0a 74 61 62 6c 65 20 79 6f 75 |giant..table you| 00000790 72 73 65 6c 66 20 77 69 74 68 6f 75 74 20 75 73 |rself without us| 000007a0 69 6e 67 20 74 68 65 20 63 6f 6d 70 75 74 65 72 |ing the computer| 000007b0 27 73 20 67 65 6e 65 72 61 6c 20 70 75 72 70 6f |'s general purpo| 000007c0 73 65 20 67 72 61 70 68 69 63 73 0d 0a 63 6f 6d |se graphics..com| 000007d0 6d 61 6e 64 73 2c 20 79 6f 75 20 63 61 6e 20 67 |mands, you can g| 000007e0 65 74 20 65 78 61 63 74 6c 79 20 74 68 65 20 72 |et exactly the r| 000007f0 65 73 75 6c 74 20 74 68 61 74 20 79 6f 75 20 77 |esult that you w| 00000800 61 6e 74 2c 20 61 6e 64 20 6d 75 63 68 20 66 61 |ant, and much fa| 00000810 73 74 65 72 0d 0a 74 68 61 6e 20 79 6f 75 20 77 |ster..than you w| 00000820 6f 75 6c 64 20 61 63 68 69 65 76 65 20 69 66 20 |ould achieve if | 00000830 79 6f 75 20 77 65 72 65 20 64 6f 69 6e 67 20 74 |you were doing t| 00000840 68 65 20 6f 70 65 72 61 74 69 6f 6e 20 74 68 72 |he operation thr| 00000850 6f 75 67 68 20 74 68 65 0d 0a 63 6f 6d 70 75 74 |ough the..comput| 00000860 65 72 27 73 20 63 6f 6d 6d 61 6e 64 73 2e 20 54 |er's commands. T| 00000870 68 65 73 65 20 68 61 76 65 20 74 6f 20 70 72 6f |hese have to pro| 00000880 63 65 73 73 20 74 68 65 20 70 61 72 61 6d 65 74 |cess the paramet| 00000890 65 72 73 20 77 68 69 63 68 20 79 6f 75 20 67 69 |ers which you gi| 000008a0 76 65 2c 0d 0a 61 6e 64 20 74 68 65 6e 20 63 61 |ve,..and then ca| 000008b0 6c 63 75 6c 61 74 65 20 77 68 65 72 65 20 61 62 |lculate where ab| 000008c0 6f 75 74 73 20 69 6e 20 74 68 65 20 67 69 61 6e |outs in the gian| 000008d0 74 20 74 61 62 6c 65 20 79 6f 75 20 77 61 6e 74 |t table you want| 000008e0 20 74 6f 20 61 6c 74 65 72 2c 0d 0a 62 65 66 6f | to alter,..befo| 000008f0 72 65 20 74 68 65 79 20 63 61 6e 20 61 63 74 75 |re they can actu| 00000900 61 6c 6c 79 20 64 6f 20 61 6e 79 20 75 73 65 66 |ally do any usef| 00000910 75 6c 20 77 6f 72 6b 2e 20 54 68 75 73 20 61 20 |ul work. Thus a | 00000920 6c 6f 74 20 6f 66 20 63 6f 6d 70 75 74 65 72 20 |lot of computer | 00000930 74 69 6d 65 0d 0a 69 73 20 77 61 73 74 65 64 20 |time..is wasted | 00000940 69 6e 20 70 65 72 66 6f 72 6d 69 6e 67 20 63 61 |in performing ca| 00000950 6c 63 75 6c 61 74 69 6f 6e 73 2c 20 77 68 69 63 |lculations, whic| 00000960 68 20 63 61 6e 20 61 63 74 75 61 6c 6c 79 20 62 |h can actually b| 00000970 65 20 73 6b 69 70 70 65 64 20 69 66 20 74 68 65 |e skipped if the| 00000980 0d 0a 70 72 6f 67 72 61 6d 6d 65 72 20 69 73 20 |..programmer is | 00000990 63 61 72 65 66 75 6c 2e 0d 0a 0d 0a 54 68 65 72 |careful.....Ther| 000009a0 65 20 61 72 65 20 74 77 6f 20 70 6f 73 73 69 62 |e are two possib| 000009b0 6c 65 20 77 61 79 73 20 6f 66 20 61 63 68 69 65 |le ways of achie| 000009c0 76 69 6e 67 20 74 68 69 73 20 69 64 65 61 2c 20 |ving this idea, | 000009d0 62 6f 74 68 20 6f 66 20 77 68 69 63 68 20 61 72 |both of which ar| 000009e0 65 20 75 73 65 66 75 6c 0d 0a 69 6e 20 64 69 66 |e useful..in dif| 000009f0 66 65 72 65 6e 74 20 73 69 74 75 61 74 69 6f 6e |ferent situation| 00000a00 73 3a 0d 0a 0d 0a 31 2e 20 53 61 76 65 20 73 63 |s:....1. Save sc| 00000a10 72 65 65 6e 20 6d 65 6d 6f 72 79 20 74 6f 20 64 |reen memory to d| 00000a20 69 73 63 2e 0d 0a 0d 0a 54 68 69 73 20 69 64 65 |isc.....This ide| 00000a30 61 20 69 73 20 66 61 69 72 6c 79 20 73 69 6d 70 |a is fairly simp| 00000a40 6c 65 20 74 6f 20 75 6e 64 65 72 73 74 61 6e 64 |le to understand| 00000a50 2e 20 59 6f 75 2c 20 61 73 20 74 68 65 20 70 72 |. You, as the pr| 00000a60 6f 67 72 61 6d 6d 65 72 2c 20 77 72 69 74 65 20 |ogrammer, write | 00000a70 61 0d 0a 70 72 6f 67 72 61 6d 20 74 6f 20 70 6c |a..program to pl| 00000a80 6f 74 20 74 68 65 20 61 72 74 77 6f 72 6b 20 66 |ot the artwork f| 00000a90 6f 72 20 79 6f 75 72 20 70 72 6f 67 72 61 6d 20 |or your program | 00000aa0 6f 6e 74 6f 20 74 68 65 20 73 63 72 65 65 6e 2c |onto the screen,| 00000ab0 20 74 61 6b 69 6e 67 0d 0a 68 6f 77 65 76 65 72 | taking..however| 00000ac0 20 6d 61 6e 79 20 68 6f 75 72 73 20 69 74 20 6d | many hours it m| 00000ad0 61 79 20 74 61 6b 65 20 74 6f 20 63 6f 6d 70 6c |ay take to compl| 00000ae0 65 74 65 20 61 6c 6c 20 6f 66 20 74 68 65 20 63 |ete all of the c| 00000af0 61 6c 63 75 6c 61 74 69 6f 6e 73 0d 0a 72 65 71 |alculations..req| 00000b00 75 69 72 65 64 20 74 6f 20 70 6c 6f 74 20 74 68 |uired to plot th| 00000b10 65 20 67 72 61 70 68 69 63 73 2e 20 59 6f 75 20 |e graphics. You | 00000b20 72 75 6e 20 74 68 69 73 20 70 72 6f 67 72 61 6d |run this program| 00000b30 20 6f 6e 63 65 20 6f 6e 20 79 6f 75 72 20 63 6f | once on your co| 00000b40 6d 70 75 74 65 72 2c 0d 0a 73 6f 20 74 68 61 74 |mputer,..so that| 00000b50 20 79 6f 75 72 20 6d 61 73 74 65 72 70 69 65 63 | your masterpiec| 00000b60 65 20 69 73 20 73 74 6f 72 65 64 20 69 6e 20 74 |e is stored in t| 00000b70 68 65 20 73 63 72 65 65 6e 20 6d 65 6d 6f 72 79 |he screen memory| 00000b80 20 6f 66 20 79 6f 75 72 20 63 6f 6d 70 75 74 65 | of your compute| 00000b90 72 0d 0a 28 69 65 2e 20 69 73 20 6f 6e 20 74 68 |r..(ie. is on th| 00000ba0 65 20 6d 6f 6e 69 74 6f 72 20 6f 66 20 79 6f 75 |e monitor of you| 00000bb0 72 20 63 6f 6d 70 75 74 65 72 29 2e 20 59 6f 75 |r computer). You| 00000bc0 20 74 68 61 6e 20 74 72 61 6e 73 66 65 72 20 74 | than transfer t| 00000bd0 68 65 20 65 6e 74 69 72 65 0d 0a 63 6f 6e 74 65 |he entire..conte| 00000be0 6e 74 73 20 6f 66 20 74 68 65 20 73 63 72 65 65 |nts of the scree| 00000bf0 6e 20 6d 65 6d 6f 72 79 20 6f 6e 20 79 6f 75 72 |n memory on your| 00000c00 20 63 6f 6d 70 75 74 65 72 20 74 6f 20 66 6c 6f | computer to flo| 00000c10 70 70 79 20 64 69 73 63 2e 0d 0a 0d 0a 54 68 65 |ppy disc.....The| 00000c20 6e 2c 20 69 6e 20 74 68 65 20 66 69 6e 61 6c 20 |n, in the final | 00000c30 70 72 6f 67 72 61 6d 20 77 68 69 63 68 20 79 6f |program which yo| 00000c40 75 20 77 61 6e 74 20 74 68 65 20 75 73 65 72 20 |u want the user | 00000c50 74 6f 20 6f 70 65 72 61 74 65 2c 20 79 6f 75 20 |to operate, you | 00000c60 69 6e 63 6c 75 64 65 0d 0a 61 20 63 6f 6d 6d 61 |include..a comma| 00000c70 6e 64 20 74 6f 20 6c 6f 61 64 20 74 68 69 73 20 |nd to load this | 00000c80 64 61 74 61 20 62 61 63 6b 20 66 72 6f 6d 20 66 |data back from f| 00000c90 6c 6f 70 70 79 20 64 69 73 63 20 69 6e 74 6f 20 |loppy disc into | 00000ca0 74 68 65 20 73 63 72 65 65 6e 20 6d 65 6d 6f 72 |the screen memor| 00000cb0 79 0d 0a 6f 66 20 74 68 65 69 72 20 63 6f 6d 70 |y..of their comp| 00000cc0 75 74 65 72 2e 20 49 6e 20 61 20 6d 61 74 74 65 |uter. In a matte| 00000cd0 72 20 6f 66 20 61 20 63 6f 75 70 6c 65 20 6f 66 |r of a couple of| 00000ce0 20 73 65 63 6f 6e 64 73 2c 20 67 72 61 70 68 69 | seconds, graphi| 00000cf0 63 73 20 77 68 69 63 68 20 74 6f 6f 6b 0d 0a 70 |cs which took..p| 00000d00 6f 73 73 69 62 6c 65 20 68 6f 75 72 73 20 74 6f |ossible hours to| 00000d10 20 63 61 6c 63 75 6c 61 74 65 20 77 69 6c 6c 20 | calculate will | 00000d20 61 70 70 65 61 72 20 6f 6e 20 74 68 65 69 72 20 |appear on their | 00000d30 73 63 72 65 65 6e 2e 20 54 68 69 73 20 69 73 20 |screen. This is | 00000d40 61 0d 0a 74 65 63 68 6e 69 71 75 65 20 77 68 69 |a..technique whi| 00000d50 63 68 20 49 20 68 61 76 65 20 75 73 65 64 20 69 |ch I have used i| 00000d60 6e 20 73 65 76 65 72 61 6c 20 6f 66 20 6d 79 20 |n several of my | 00000d70 70 72 6f 67 72 61 6d 73 2e 20 54 68 65 20 6d 61 |programs. The ma| 00000d80 69 6e 20 6d 65 6e 75 20 6f 66 0d 0a 53 68 69 70 |in menu of..Ship| 00000d90 77 72 65 63 6b 65 64 20 49 49 3a 20 4a 75 70 69 |wrecked II: Jupi| 00000da0 74 65 72 20 33 2c 20 77 68 65 72 65 20 79 6f 75 |ter 3, where you| 00000db0 20 73 65 6c 65 63 74 20 50 6c 61 79 2c 20 49 6e | select Play, In| 00000dc0 73 74 72 75 63 74 69 6f 6e 73 2c 20 47 61 6d 65 |structions, Game| 00000dd0 0d 0a 43 6f 6d 70 6c 65 74 65 20 6f 72 20 43 68 |..Complete or Ch| 00000de0 65 61 74 20 77 69 74 68 20 74 68 65 20 73 74 61 |eat with the sta| 00000df0 72 66 69 65 6c 64 20 62 61 63 6b 64 72 6f 70 20 |rfield backdrop | 00000e00 77 61 73 20 64 6f 6e 65 20 69 6e 20 74 68 69 73 |was done in this| 00000e10 20 77 61 79 20 2d 20 74 68 65 0d 0a 73 63 72 65 | way - the..scre| 00000e20 65 6e 20 74 6f 6f 6b 20 6e 65 61 72 6c 79 20 61 |en took nearly a| 00000e30 6e 20 68 6f 75 72 20 66 6f 72 20 6d 79 20 63 6f |n hour for my co| 00000e40 6d 70 75 74 65 72 20 74 6f 20 63 61 6c 63 75 6c |mputer to calcul| 00000e50 61 74 65 2c 20 62 75 74 20 49 20 77 61 73 20 61 |ate, but I was a| 00000e60 62 6c 65 0d 0a 74 6f 20 6d 61 6b 65 20 69 74 20 |ble..to make it | 00000e70 61 70 70 65 61 72 20 69 6e 20 73 65 63 6f 6e 64 |appear in second| 00000e80 73 20 6f 6e 20 79 6f 75 72 20 73 63 72 65 65 6e |s on your screen| 00000e90 2e 20 49 20 73 68 6f 75 6c 64 20 61 6c 73 6f 20 |. I should also | 00000ea0 6d 65 6e 74 69 6f 6e 20 74 68 65 20 74 69 74 6c |mention the titl| 00000eb0 65 0d 0a 73 63 72 65 65 6e 20 74 6f 20 53 68 69 |e..screen to Shi| 00000ec0 70 77 72 65 63 6b 20 77 69 74 68 20 74 68 65 20 |pwreck with the | 00000ed0 61 6e 69 6d 61 74 65 64 20 73 65 61 2c 20 6e 6f |animated sea, no| 00000ee0 74 20 74 6f 20 6d 65 6e 74 69 6f 6e 20 74 68 65 |t to mention the| 00000ef0 20 65 6e 64 6c 65 73 73 20 45 55 47 0d 0a 74 69 | endless EUG..ti| 00000f00 74 6c 65 20 73 63 72 65 65 6e 73 20 49 20 68 61 |tle screens I ha| 00000f10 76 65 20 64 6f 6e 65 20 69 6e 20 74 68 69 73 20 |ve done in this | 00000f20 77 61 79 20 2d 20 74 68 65 20 43 68 72 69 73 74 |way - the Christ| 00000f30 6d 61 73 20 45 55 47 20 33 35 20 73 63 72 65 65 |mas EUG 35 scree| 00000f40 6e 20 77 69 74 68 0d 0a 74 68 65 20 73 77 69 72 |n with..the swir| 00000f50 6c 79 20 62 6c 75 65 20 62 61 63 6b 67 72 6f 75 |ly blue backgrou| 00000f60 6e 64 20 28 63 72 65 64 69 74 65 64 20 65 72 72 |nd (credited err| 00000f70 6f 6e 65 6f 75 73 6c 79 20 74 6f 20 52 6f 62 65 |oneously to Robe| 00000f80 72 74 20 53 70 72 6f 77 73 6f 6e 29 20 74 6f 6f |rt Sprowson) too| 00000f90 6b 0d 0a 74 77 6f 20 77 68 6f 6c 65 20 64 61 79 |k..two whole day| 00000fa0 73 20 74 6f 20 70 6c 6f 74 21 0d 0a 0d 0a 49 6e |s to plot!....In| 00000fb0 20 6f 72 64 65 72 20 74 6f 20 61 63 68 69 65 76 | order to achiev| 00000fc0 65 20 74 68 69 73 2c 20 79 6f 75 20 73 69 6d 70 |e this, you simp| 00000fd0 6c 79 20 6e 65 65 64 20 74 6f 20 75 6e 64 65 72 |ly need to under| 00000fe0 73 74 61 6e 64 20 74 77 6f 20 42 41 53 49 43 20 |stand two BASIC | 00000ff0 63 6f 6d 6d 61 6e 64 73 3a 0d 0a 0d 0a 2a 53 41 |commands:....*SA| 00001000 56 45 20 46 69 6c 65 6e 61 6d 65 20 6e 6e 6e 6e |VE Filename nnnn| 00001010 20 6d 6d 6d 6d 0d 0a 2a 4c 4f 41 44 20 46 69 6c | mmmm..*LOAD Fil| 00001020 65 6e 61 6d 65 20 6e 6e 6e 6e 0d 0a 0d 0a 54 68 |ename nnnn....Th| 00001030 65 73 65 20 6c 6f 61 64 20 61 6e 64 20 73 61 76 |ese load and sav| 00001040 65 20 61 72 65 61 73 20 6f 66 20 74 68 65 20 63 |e areas of the c| 00001050 6f 6d 70 75 74 65 72 27 73 20 6d 65 6d 6f 72 79 |omputer's memory| 00001060 20 74 6f 20 66 6c 6f 70 70 79 20 64 69 73 63 20 | to floppy disc | 00001070 6f 72 20 63 61 73 73 65 74 74 65 0d 0a 77 69 74 |or cassette..wit| 00001080 68 20 74 68 65 20 66 69 6c 65 6e 61 6d 65 20 67 |h the filename g| 00001090 69 76 61 6e 20 69 6e 20 70 6c 61 63 65 20 6f 66 |ivan in place of| 000010a0 20 74 68 65 20 77 6f 72 6b 20 46 69 6c 65 6e 61 | the work Filena| 000010b0 6d 65 2c 20 73 74 61 72 74 69 6e 67 20 61 74 20 |me, starting at | 000010c0 6d 65 6d 6f 72 79 0d 0a 6c 6f 63 61 74 69 6f 6e |memory..location| 000010d0 20 6e 6e 6e 6e 2c 20 61 6e 64 20 63 6f 6e 74 69 | nnnn, and conti| 000010e0 6e 75 69 6e 67 20 75 6e 74 69 6c 20 6d 65 6d 6f |nuing until memo| 000010f0 72 79 20 6c 6f 63 61 74 69 6f 6e 20 6d 6d 6d 6d |ry location mmmm| 00001100 20 28 77 68 65 72 65 20 6e 6e 6e 6e 20 61 6e 64 | (where nnnn and| 00001110 20 6d 6d 6d 6d 0d 0a 61 72 65 20 62 6f 74 68 20 | mmmm..are both | 00001120 69 6e 20 68 65 78 69 64 65 63 69 6d 61 6c 20 2d |in hexidecimal -| 00001130 20 62 61 73 65 20 31 36 29 2e 20 44 6f 6e 27 74 | base 16). 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The | 00001270 6c 6f 63 61 74 69 6f 6e 20 6f 66 20 74 68 65 73 |location of thes| 00001280 65 0d 0a 77 69 74 68 69 6e 20 79 6f 75 72 20 63 |e..within your c| 00001290 6f 6d 70 75 74 65 72 20 76 61 72 69 65 73 20 64 |omputer varies d| 000012a0 65 70 65 64 69 6e 67 20 75 70 6f 6e 20 77 68 69 |epeding upon whi| 000012b0 63 68 20 67 72 61 70 68 69 63 73 20 6d 6f 64 65 |ch graphics mode| 000012c0 20 79 6f 75 20 61 72 65 20 75 73 69 6e 67 0d 0a | you are using..| 000012d0 28 77 68 69 63 68 20 79 6f 75 20 73 65 6c 65 63 |(which you selec| 000012e0 74 65 64 20 75 73 69 6e 67 20 74 68 65 20 4d 4f |ted using the MO| 000012f0 44 45 20 63 6f 6d 6d 61 6e 64 20 2d 20 73 65 65 |DE command - see| 00001300 20 70 72 65 76 69 6f 75 73 20 74 75 74 6f 72 69 | previous tutori| 00001310 61 6c 20 69 66 20 79 6f 75 0d 0a 61 72 65 20 75 |al if you..are u| 00001320 6e 73 75 72 65 20 6f 66 20 77 68 61 74 20 74 68 |nsure of what th| 00001330 69 73 20 69 73 29 2c 20 62 75 74 20 69 73 20 61 |is is), but is a| 00001340 6c 77 61 79 73 20 63 6f 6e 73 74 61 6e 74 20 66 |lways constant f| 00001350 6f 72 20 61 6e 79 20 70 61 72 74 69 63 75 6c 61 |or any particula| 00001360 72 0d 0a 6d 6f 64 65 2e 20 74 68 65 20 76 61 6c |r..mode. the val| 00001370 75 65 73 20 66 6f 72 20 74 68 65 20 64 69 66 66 |ues for the diff| 00001380 65 72 65 6e 74 20 6d 6f 64 65 73 20 61 72 65 20 |erent modes are | 00001390 67 69 76 65 6e 20 62 65 6c 6f 77 3a 0d 0a 0d 0a |given below:....| 000013a0 4d 6f 64 65 20 20 20 20 20 20 20 20 20 20 20 20 |Mode | 000013b0 6e 6e 6e 6e 20 20 20 20 6d 6d 6d 6d 20 20 20 4e |nnnn mmmm N| 000013c0 4f 54 45 53 3a 0d 0a 30 20 20 20 20 20 20 20 20 |OTES:..0 | 000013d0 20 20 20 20 20 20 20 33 30 30 30 20 20 20 20 37 | 3000 7| 000013e0 46 46 46 0d 0a 31 20 20 20 20 20 20 20 20 20 20 |FFF..1 | 000013f0 20 20 20 20 20 33 30 30 30 20 20 20 20 37 46 46 | 3000 7FF| 00001400 46 20 20 20 2d 20 6e 6e 6e 6e 20 61 6e 64 20 6d |F - nnnn and m| 00001410 6d 6d 6d 20 76 61 6c 75 65 73 20 67 69 76 65 6e |mmm values given| 00001420 20 74 6f 20 74 68 65 20 6c 65 66 74 20 61 72 65 | to the left are| 00001430 0d 0a 32 20 20 20 20 20 20 20 20 20 20 20 20 20 |..2 | 00001440 20 20 33 30 30 30 20 20 20 20 37 46 46 46 20 20 | 3000 7FFF | 00001450 20 61 6c 6c 20 69 6e 20 68 65 78 69 64 65 63 69 | all in hexideci| 00001460 6d 61 6c 2e 20 54 68 65 72 65 66 6f 72 65 20 74 |mal. Therefore t| 00001470 68 65 79 20 63 61 6e 20 62 65 0d 0a 33 20 20 20 |hey can be..3 | 00001480 20 20 20 20 20 20 20 20 20 20 20 20 34 30 30 30 | 4000| 00001490 20 20 20 20 37 46 46 46 20 20 20 73 75 62 73 74 | 7FFF subst| 000014a0 69 74 75 74 65 64 20 64 69 72 65 63 74 6c 79 20 |ituted directly | 000014b0 69 6e 74 6f 20 74 68 65 20 2a 4c 4f 41 44 20 61 |into the *LOAD a| 000014c0 6e 64 20 2a 53 41 56 45 0d 0a 34 20 20 20 20 20 |nd *SAVE..4 | 000014d0 20 20 20 20 20 20 20 20 20 20 35 38 30 30 20 20 | 5800 | 000014e0 20 20 37 46 46 46 20 20 20 63 6f 6d 6d 61 6e 64 | 7FFF command| 000014f0 73 20 77 69 74 68 20 6e 6f 20 63 6f 6e 76 65 72 |s with no conver| 00001500 73 69 6f 6e 20 72 65 71 75 69 72 65 64 2e 0d 0a |sion required...| 00001510 35 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 |5 | 00001520 35 38 30 30 20 20 20 20 37 46 46 46 0d 0a 36 20 |5800 7FFF..6 | 00001530 20 20 20 20 20 20 20 20 20 20 20 20 20 20 36 30 | 60| 00001540 30 30 20 20 20 20 37 46 46 46 20 20 20 2d 20 56 |00 7FFF - V| 00001550 61 6c 75 65 73 20 61 72 65 20 6e 6f 74 20 76 61 |alues are not va| 00001560 6c 69 64 20 66 6f 72 20 74 68 65 20 42 42 43 20 |lid for the BBC | 00001570 6d 6f 64 65 6c 20 41 20 69 6e 0d 0a 37 20 20 20 |model A in..7 | 00001580 20 20 20 20 20 20 20 20 20 20 20 20 37 43 30 30 | 7C00| 00001590 20 20 20 20 37 46 46 46 20 20 20 6d 6f 64 65 73 | 7FFF modes| 000015a0 20 34 2c 35 2c 36 20 6f 72 20 37 2e 0d 0a 0d 0a | 4,5,6 or 7.....| 000015b0 45 78 61 6d 70 6c 65 73 3a 0d 0a 0d 0a 53 75 70 |Examples:....Sup| 000015c0 70 6f 73 65 20 79 6f 75 20 61 72 65 20 69 6e 20 |pose you are in | 000015d0 6d 6f 64 65 20 32 2c 20 61 6e 64 20 77 61 6e 74 |mode 2, and want| 000015e0 20 74 6f 20 73 74 6f 72 65 20 74 68 65 20 73 63 | to store the sc| 000015f0 72 65 65 6e 20 74 6f 20 61 20 66 6c 6f 70 70 79 |reen to a floppy| 00001600 2e 20 46 72 6f 6d 0d 0a 74 68 65 20 74 61 62 6c |. 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I..| 00003e40 20 20 20 20 20 20 20 20 20 20 75 73 65 20 74 68 | use th| 00003e50 65 20 73 74 61 6e 64 61 72 64 20 41 63 6f 72 6e |e standard Acorn| 00003e60 20 27 26 27 20 70 72 65 66 69 78 20 74 6f 20 69 | '&' prefix to i| 00003e70 6e 64 69 63 61 74 65 20 68 65 78 69 64 65 63 69 |ndicate hexideci| 00003e80 6d 61 6c 20 76 61 6c 75 65 73 2e 0d 0a 20 20 20 |mal values... | 00003e90 20 20 20 20 20 20 20 54 68 6f 73 65 20 75 73 65 | Those use| 00003ea0 64 20 74 6f 20 64 65 61 6c 69 6e 67 20 77 69 74 |d to dealing wit| 00003eb0 68 20 50 43 73 20 61 72 65 20 61 6e 79 20 6f 74 |h PCs are any ot| 00003ec0 68 65 72 20 63 6f 6d 70 75 74 65 72 73 20 6d 61 |her computers ma| 00003ed0 79 20 62 65 20 75 73 65 64 0d 0a 20 20 20 20 20 |y be used.. | 00003ee0 20 20 20 20 20 74 6f 20 74 68 65 20 41 6d 65 72 | to the Amer| 00003ef0 69 63 61 6e 20 63 6f 6e 76 65 6e 74 69 6f 6e 20 |ican convention | 00003f00 6f 66 20 75 73 69 6e 67 20 61 20 64 6f 6c 6c 61 |of using a dolla| 00003f10 72 20 70 72 65 66 69 78 20 69 6e 20 69 74 73 20 |r prefix in its | 00003f20 70 6c 61 63 65 2e 0d 0a 20 20 20 20 20 20 20 20 |place... | 00003f30 20 20 49 74 20 73 68 6f 75 6c 64 20 62 65 20 6e | It should be n| 00003f40 6f 74 65 64 20 74 68 61 74 20 74 68 65 20 45 6c |oted that the El| 00003f50 6b 20 65 78 70 65 63 74 73 20 26 20 61 6e 64 20 |k expects & and | 00003f60 77 69 6c 6c 20 6e 6f 74 20 61 63 63 65 70 74 20 |will not accept | 00003f70 24 2e 0d 0a 0d 0a 45 78 61 6d 70 6c 65 3a 0d 0a |$.....Example:..| 00003f80 0d 0a 53 75 70 70 6f 73 65 20 49 20 77 61 6e 74 |..Suppose I want| 00003f90 20 74 6f 20 64 72 61 77 20 61 20 62 6c 6f 62 20 | to draw a blob | 00003fa0 69 6e 20 63 68 61 72 61 63 74 65 72 20 73 71 75 |in character squ| 00003fb0 61 72 65 20 28 36 2c 37 29 2c 20 69 6e 20 6d 6f |are (6,7), in mo| 00003fc0 64 65 20 31 2e 20 57 68 61 74 20 69 73 20 0d 0a |de 1. What is ..| 00003fd0 74 68 65 20 61 64 64 72 65 73 73 20 6f 66 20 74 |the address of t| 00003fe0 68 69 73 20 73 71 75 61 72 65 3f 20 28 67 69 76 |his square? (giv| 00003ff0 65 6e 20 74 68 61 74 20 65 61 63 68 20 63 68 61 |en that each cha| 00004000 72 61 63 74 65 72 20 74 61 6b 65 73 20 31 36 20 |racter takes 16 | 00004010 62 79 74 65 73 20 6f 66 0d 0a 73 63 72 65 65 6e |bytes of..screen| 00004020 20 6d 65 6d 6f 72 79 20 74 6f 20 64 65 66 69 6e | memory to defin| 00004030 65 20 69 6e 20 6d 6f 64 65 20 31 20 2d 20 77 65 |e in mode 1 - we| 00004040 27 6c 6c 20 63 6f 6d 65 20 74 6f 20 68 6f 77 20 |'ll come to how | 00004050 74 6f 20 63 61 6c 63 75 6c 61 74 65 20 74 68 69 |to calculate thi| 00004060 73 20 69 6e 0d 0a 61 20 6d 69 6e 75 74 65 29 2e |s in..a minute).| 00004070 0d 0a 0d 0a 57 65 6c 6c 20 2d 20 6c 6f 6f 6b 69 |....Well - looki| 00004080 6e 67 20 61 74 20 74 68 65 20 74 61 62 6c 65 20 |ng at the table | 00004090 65 61 72 6c 69 65 72 2c 20 73 63 72 65 65 6e 20 |earlier, screen | 000040a0 6d 65 6d 6f 72 79 20 73 74 61 72 74 73 20 61 74 |memory starts at| 000040b0 20 26 33 30 30 30 20 69 6e 20 6d 6f 64 65 20 31 | &3000 in mode 1| 000040c0 2e 0d 0a 57 65 20 77 61 6e 74 20 74 6f 20 66 69 |...We want to fi| 000040d0 6e 64 20 74 68 65 20 73 74 61 72 74 20 6f 66 20 |nd the start of | 000040e0 72 6f 77 20 37 20 69 6e 20 73 63 72 65 65 6e 20 |row 7 in screen | 000040f0 6d 65 6d 6f 72 79 2e 20 54 68 69 73 20 72 6f 77 |memory. This row| 00004100 20 68 61 73 20 37 20 72 6f 77 73 20 6f 66 0d 0a | has 7 rows of..| 00004110 63 68 61 72 61 63 74 65 72 73 20 61 62 6f 76 65 |characters above| 00004120 20 69 74 2c 20 61 6e 64 20 77 68 69 63 68 20 77 | it, and which w| 00004130 69 6c 6c 20 62 65 20 73 74 6f 72 65 64 20 62 65 |ill be stored be| 00004140 66 6f 72 65 20 69 74 2e 20 45 61 63 68 20 6f 66 |fore it. Each of| 00004150 20 74 68 65 73 65 20 72 6f 77 73 0d 0a 63 6f 6e | these rows..con| 00004160 73 69 73 74 73 20 6f 66 20 34 30 20 63 68 61 72 |sists of 40 char| 00004170 61 63 74 65 72 73 2c 20 77 68 69 63 68 20 74 61 |acters, which ta| 00004180 6b 65 20 75 70 20 31 36 20 62 79 74 65 73 20 65 |ke up 16 bytes e| 00004190 61 63 68 2e 20 54 68 65 72 65 66 6f 72 65 20 74 |ach. Therefore t| 000041a0 68 65 20 74 6f 74 61 6c 0d 0a 6d 65 6d 6f 72 79 |he total..memory| 000041b0 20 74 61 6b 65 6e 20 75 70 20 62 79 20 74 68 65 | taken up by the| 000041c0 73 65 20 72 6f 77 73 20 69 73 20 37 20 2a 20 34 |se rows is 7 * 4| 000041d0 30 20 2a 20 31 36 20 3d 20 34 34 38 30 20 62 79 |0 * 16 = 4480 by| 000041e0 74 65 73 2e 20 5b 45 61 63 68 20 63 68 61 72 61 |tes. [Each chara| 000041f0 63 74 65 72 0d 0a 69 73 20 31 36 20 62 79 74 65 |cter..is 16 byte| 00004200 73 2c 20 65 61 63 68 20 72 6f 77 20 63 6f 6e 73 |s, each row cons| 00004210 69 73 74 73 20 6f 66 20 34 30 20 6f 66 20 74 68 |ists of 40 of th| 00004220 65 73 65 20 63 68 61 72 61 63 74 65 72 73 2c 20 |ese characters, | 00004230 74 68 65 72 65 66 6f 72 65 20 77 65 0d 0a 6d 75 |therefore we..mu| 00004240 6c 74 69 70 6c 79 20 62 79 20 34 30 2c 20 61 6e |ltiply by 40, an| 00004250 64 20 61 73 20 74 68 65 72 65 20 61 72 65 20 37 |d as there are 7| 00004260 20 6f 66 20 74 68 65 73 65 20 63 6f 6d 70 6c 65 | of these comple| 00004270 74 65 20 72 6f 77 73 2c 20 77 65 20 6d 75 6c 74 |te rows, we mult| 00004280 69 70 6c 79 20 62 79 0d 0a 37 20 74 6f 20 67 65 |iply by..7 to ge| 00004290 74 20 74 68 65 20 76 61 6c 75 65 20 66 6f 72 20 |t the value for | 000042a0 73 65 76 65 6e 20 6f 66 20 74 68 65 73 65 20 72 |seven of these r| 000042b0 6f 77 73 5d 0d 0a 0d 0a 4e 6f 77 20 77 65 20 68 |ows]....Now we h| 000042c0 61 76 65 20 74 68 61 74 20 74 68 65 20 73 74 61 |ave that the sta| 000042d0 72 74 69 6e 67 20 61 64 64 72 65 73 73 20 6f 66 |rting address of| 000042e0 20 72 6f 77 20 37 20 69 73 20 61 74 3a 0d 0a 0d | row 7 is at:...| 000042f0 0a 26 33 30 30 30 20 2b 20 34 34 38 30 20 3d 20 |.&3000 + 4480 = | 00004300 26 34 31 38 30 0d 0a 0d 0a 4e 6f 77 20 74 68 61 |&4180....Now tha| 00004310 74 20 77 65 20 68 61 76 65 20 66 6f 75 6e 64 20 |t we have found | 00004320 77 68 65 72 65 20 61 62 6f 75 74 73 20 69 6e 20 |where abouts in | 00004330 6d 65 6d 6f 72 79 20 74 68 69 73 20 72 6f 77 20 |memory this row | 00004340 73 74 61 72 74 73 2c 20 77 65 20 6e 65 65 64 20 |starts, we need | 00004350 74 6f 0d 0a 6c 6f 63 61 74 65 20 63 68 61 72 61 |to..locate chara| 00004360 63 74 65 72 20 36 2e 20 54 68 69 73 20 73 68 6f |cter 6. This sho| 00004370 75 6c 64 20 62 65 20 66 61 69 72 6c 79 20 65 61 |uld be fairly ea| 00004380 73 79 20 2d 20 77 65 20 6b 6e 6f 77 20 74 68 61 |sy - we know tha| 00004390 74 20 63 68 61 72 61 63 74 65 72 73 20 61 72 65 |t characters are| 000043a0 0d 0a 73 74 6f 72 65 64 20 66 72 6f 6d 20 6c 65 |..stored from le| 000043b0 66 74 20 74 6f 20 72 69 67 68 74 2c 20 73 6f 20 |ft to right, so | 000043c0 6a 75 73 74 20 61 64 64 20 6f 6e 20 74 68 65 20 |just add on the | 000043d0 6d 65 6d 6f 72 79 20 72 65 71 75 69 72 65 64 20 |memory required | 000043e0 74 6f 20 73 74 6f 72 65 20 73 69 78 0d 0a 63 68 |to store six..ch| 000043f0 61 72 61 63 74 65 72 73 20 74 6f 20 74 68 65 20 |aracters to the | 00004400 6c 65 66 74 20 6f 66 20 74 68 65 20 6f 6e 65 20 |left of the one | 00004410 77 65 20 77 61 6e 74 2c 20 69 2e 65 2e 20 31 36 |we want, i.e. 16| 00004420 20 2a 20 36 20 3d 20 39 36 20 62 79 74 65 73 20 | * 6 = 96 bytes | 00004430 5b 53 69 78 0d 0a 63 68 61 72 61 63 74 65 72 73 |[Six..characters| 00004440 2c 20 65 61 63 68 20 74 61 6b 69 6e 67 20 31 36 |, each taking 16| 00004450 20 62 79 74 65 73 20 74 6f 20 73 74 6f 72 65 5d | bytes to store]| 00004460 2e 0d 0a 0d 0a 54 68 65 72 65 66 6f 72 65 20 74 |.....Therefore t| 00004470 68 65 20 61 64 64 72 65 73 73 20 6f 66 20 63 68 |he address of ch| 00004480 61 72 61 63 74 65 72 20 28 36 2c 37 29 20 77 69 |aracter (6,7) wi| 00004490 6c 6c 20 62 65 3a 0d 0a 0d 0a 26 34 31 38 30 20 |ll be:....&4180 | 000044a0 2b 20 39 36 20 3d 20 26 34 31 45 30 0d 0a 0d 0a |+ 96 = &41E0....| 000044b0 41 6e 73 77 65 72 3a 20 43 68 61 72 61 63 74 65 |Answer: Characte| 000044c0 72 20 28 36 2c 37 29 20 69 73 20 73 74 6f 72 65 |r (6,7) is store| 000044d0 64 20 66 72 6f 6d 20 26 34 31 45 30 20 74 6f 20 |d from &41E0 to | 000044e0 26 34 31 45 46 0d 0a 0d 0a 4a 75 73 74 20 74 6f |&41EF....Just to| 000044f0 20 63 68 65 63 6b 20 74 68 65 20 61 6e 73 77 65 | check the answe| 00004500 72 20 69 73 20 63 6f 72 72 65 63 74 2c 20 74 79 |r is correct, ty| 00004510 70 65 20 74 68 69 73 20 73 69 6d 70 6c 65 20 6c |pe this simple l| 00004520 6f 6f 70 3a 0d 0a 0d 0a 31 30 20 4d 4f 44 45 20 |oop:....10 MODE | 00004530 31 0d 0a 32 30 20 46 4f 52 20 61 64 3d 26 34 31 |1..20 FOR ad=&41| 00004540 45 30 20 54 4f 20 26 34 31 45 46 0d 0a 33 30 20 |E0 TO &41EF..30 | 00004550 3f 61 64 3d 32 35 35 0d 0a 34 30 20 4e 45 58 54 |?ad=255..40 NEXT| 00004560 0d 0a 0d 0a 41 6e 64 20 79 65 73 2c 20 61 20 77 |....And yes, a w| 00004570 68 69 74 65 20 73 70 6c 6f 64 67 65 20 64 6f 65 |hite splodge doe| 00004580 73 20 61 70 70 65 61 72 20 69 6e 20 73 71 75 61 |s appear in squa| 00004590 72 65 20 28 36 2c 37 29 2e 0d 0a 0d 0a 54 68 69 |re (6,7).....Thi| 000045a0 73 20 77 68 6f 6c 65 20 70 72 6f 63 65 64 75 72 |s whole procedur| 000045b0 65 20 63 61 6e 20 61 63 74 75 61 6c 6c 79 20 62 |e can actually b| 000045c0 65 20 72 65 66 69 6e 65 64 20 64 6f 77 6e 2c 20 |e refined down, | 000045d0 61 6e 64 20 65 78 70 72 65 73 73 65 64 20 61 73 |and expressed as| 000045e0 20 61 20 73 69 6d 70 6c 65 0d 0a 66 6f 72 6d 75 | a simple..formu| 000045f0 6c 61 3a 0d 0a 0d 0a 41 64 64 72 65 73 73 20 3d |la:....Address =| 00004600 20 42 61 73 65 20 2b 20 28 20 79 20 2a 20 4e 6f | Base + ( y * No| 00004610 2e 20 63 68 61 72 61 63 74 65 72 73 20 70 65 72 |. characters per| 00004620 20 6c 69 6e 65 20 2b 20 78 20 29 20 2a 20 4d 65 | line + x ) * Me| 00004630 6d 6f 72 79 20 70 65 72 20 63 68 61 72 61 63 74 |mory per charact| 00004640 65 72 0d 0a 0d 0a 57 68 65 72 65 3a 20 41 64 64 |er....Where: Add| 00004650 72 65 73 73 3d 20 54 68 65 20 6d 65 6d 6f 72 79 |ress= The memory| 00004660 20 6c 6f 63 61 74 69 6f 6e 20 6f 66 20 74 68 65 | location of the| 00004670 20 73 74 61 72 74 20 6f 66 20 74 68 65 20 63 68 | start of the ch| 00004680 61 72 61 63 74 65 72 20 79 6f 75 20 77 61 6e 74 |aracter you want| 00004690 2e 0d 0a 20 20 20 20 20 20 20 42 61 73 65 20 20 |... 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