First Steps

By Mark Hutchinson

 

Issue 32

Mar/Apr 88

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NUMBERS


This issue I thought I might explain some mathematical manipulations that have been used in previous columns. It is all very simple so you will not need to book in at your local college for an '0' level maths course!


If you did not already know, the computer contains a section of memory that you can either read or write to called random access memory (RAM) and memory that cannot be written to, called read only memory (ROM).


STORING NUMBERS IN MEMORY


RAM can be pictured as a series of little boxes, or pigeonholes, each containing a number from 0 to 255. Each number gives the computer a piece of information. As you may know from past articles, memory is made up of millions of little switches (bits) in blocks of eight (this is why your machine is termed 8-bit). Each switch has two conditions, either on or off. Mathematically, any combination of eight with two states means two to the power of eight 256 (0 to 255).


Supposing we want to store numbers greater than 255? For this we must use two memory locations. One is termed the low byte and stores the numbers 0 to 255, equivalent to the units (0 to 9) in decimal. The second is the high byte and stores the multiples of 256's, equivalent to the tens in decimal. What if we want to store 255? This can be stored just in the low byte, as can any number from 0 to 255 but if we had 256 we would store it
as 1 in the high byte and clear the low byte to zero.


As an example, I will pick a number at random 57344. This needs to be split into multiples of 256 so first I find the high byte by dividing this number by 256. The result is 224. Any remainder will be less than 256 and will be stored in the low byte. To find the remainder I multiply 224 by 256 and subtract it from 57344. In this case the remainder is zero. If you want to include this in your own programs then it will be as follows,

10 NUMBER = 57344
20 HIGHBYTE = NUMBER/256
30 LOWBYTE =NUMBER-256*HIGHBYTE

I should point out here that mathematical equations are worked out in a certain order irrespective of how they appear in a program line. In order of priority they are:

Brackets
of, e.g. a third of six division
multiplication
addition

subtraction

In line 30, therefore, the HIGHBYTE is multiplied by 256 before it is subtracted from NUMBER.


WHY STORE NUMBERS?


Why do we need to use all this at all? Well, within the RAM are certain locations called POINTERS. A pointer is a signpost. It contains a number which will point to another location in memory. So what is the point of that I hear you pun! Well, let's have an example. Location 756 is just such a pointer. It holds a number that, when multiplied by 256 will send the computer to a location where all the characters are stored. By sheer coincidence, this number just happens to be 224. Now, suppose we stored another character set at 57856. By changing the number stored in location 756 we can send the computer to 57856 for a different character set. This number is, of course, 57856/256 (226 exactly).


Now for your homework and a bit of magic. Set up your computer in a GRAPHICS 1 screen and print something on it using PRINT #6; "TEXT" (or ?#6; "TEXT" for short. As usual, you will see that the characters are in upper case, so clear the screen. Print POKE 756,226 and press RETURN. Now try printing to the screen and see what happens.


OTHER EXAMPLES


Another often used example is to lower the top of RAM to protect memory. Location 106 holds a number which relates to the amount of RAM available. This number must be multiplied by 256. Each unit is called a 'PAGE' of memory and four pages = 1K of RAM (4 times 256 = 1024 = 1K).


Let us pretend that we wish to protect 4K of memory (the protected size must be in multiples of 256). First we must find out how many pages are available by PEEKing location 106, then subtract 16 (the number of 256's in 4K) from this total and POKEing the new number into the location, i.e.

10 PAGE = PEEK(106)
20 NEWPAGE =PAGE-16

30 POKE 106,NEWPAGE

An easier way to do this is by

10 POKE 106, PEEK(106)-16

Make sure that you reset the RAM top before a graphics call. this will ensure that the new details for the display list are properly stored.


USING OFFSETS


In a previous article, I explained about the IOCB and gave some details about offsets. Rather than POKE to several different locations, having to remember each one, why not take one as a base and POKE to the base plus an offset. For example, we know that the character set starts at 57344. To change the full character set by POKEing each individual location would take 1024 lines of POKE LOCATION, DATA. The easiest way would be to take 57344 as a base and add one each time then POKE in the DATA. This is called incrementing. To do this properly, the offset or increment would have to start off at zero, not 1, otherwise the first POKE would be at 57345. We could change the base to 57343 and start the offset at 1, but when you looked up this location much later it would not make immediate sense (it is a floating point logarithm routine!).


Unfortunately, the character set is in ROM and we cannot change it. We can store a new character set in RAM though. It only needs the pointer to be changed to indicate this new location and your characters automatically change. Listing 1 is a small routine to do just that.


Some points to note. I used a location suitable for this demo. I used a flag of -1 to make sure the program finished without an error. This is not strictly necessary but it does save the annoyance of inputting too much data. Also, lines 100 and 110 could be combined as line 100 (the computer automatically keeps track of the data to be read), but I did this for clarity. Notice how the space character has been changed. Even if you cannot see the characters, type POKE 756,224 and press RETURN to get the old set back. Try new DATA and run it again.


That is all for this time. Since I have given you some hints on graphics modes and how to store them, why not read the next thrilling installment and find out how to draw some pictures?


Don't forget that you can write with any problems. Include a s.a.e. if you want a reply. Write to Mark Hutchinson, 1 Hollymount, Erinvale, Finaghy, Belfast, BT10 OGL

 

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