Chapter 1

'(incomplete)'

Numbers

The first thing you'll notice while looking through SPHERE scripts is the wide variety of ways to write numbers. Since numbers are insanely important to a SPHERE scripter, this is the first lesson in the series. By the end of the lesson, I hope that you have a general understanding of hexadecimal, decimal and binary numbering systems, and SPHERE's ways of identifying each. You will also know how to generate random numbers either from a series or from a list of choices.

The first thing you need to understand is that the way we count is not the only way to count. Our numbering system contains ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9). Therefore, at the tenth number, we have to add an extra column to the number, and reset the first column to zero (1, 2, 3, 4, 5, 6, 7, 8, 9, 10). That's why our numbering system works the way it does.

In the decimal system, without realizing it, we write our numbers to mean powers of ten. For example, if you take the number 17282 (which I just made up), and divide it down we get this:

Power of ten	4	3	2	1	0
Ten to that power	10000	1000	100	10	1
Digit	1	7	2	8	2

To reach the number 17282 from here, we simply take ten to the power of the number in the top row, multiply it by the number in the bottom row, and then add all those numbers together. We get 10000 + 7000 + 200 + 80 + 2. Obviously, this is simplistic, and we do it without even realizing we're doing it. You're probably thinking "Riiight, what does Taran think he's getting at?" Well, we aren't so special that our counting system is the only way to count.

Now, there is another numbering system that is used almost solely by computers. It only contains two numbers (1 and 0) and is therefore called the binary (meaning two) system. Binary numbers look like this: 101011101101, and you often see them in ads for computers and other electronic equipment (oftentimes they are shown streaming out of a CD player on television commercials). Digits in the binary system are called bits (short for BInary digiT)Binary numbers are almost impossible to translate to decimal directly, and so some math must be done.

Binary works in the same way, by adding powers of a number. In the case of binary, since there are two numbers in the whole system, that number is naturally two. Here are some examples of powers of two. These numbers might look familiar to some people.

Power of 2	Binary number	Decimal number
0	1	1
1	10	2
2	100	4
3	1000	8
4	10000	16
5	100000	32
6	1000000	64
7	10000000	128
8	100000000	256
9	1000000000	512
10	10000000000	1024

Ridiculous eh?  :)

We need a better system! The reason we get such strange results is because 10 is not a power of two. We need to find a system where the number base IS a power of two. The most commonly used system used is base-16, or hexadecimal. I'm sure if you've perused the SPHERE boards, you've seen the word hex floating around. No, this isn't a curse or evil spell, it's a short way of saying "hexadecimal".

Binary	Decimal	Hexadecimal
1	1	1
10	2	2
11	3	3
100	4	4
101	5	5
110	6	6
111	7	7
1000	8	8
1001	9	9
1010	10	A
1011	11	B
1100	12	C
1101	13	D
1110	14	E
1111	15	F
10000	16	10

See how it works? There are an extra six numbers added onto the end of the system, represented by the first six letters of the alphabet.

Now, in SPHERE scripting, you are almost NEVER going to be dealing with binary numbers that are NOT powers of two, and if you do, you can simply use any scientific calculator to figure it out. But it's a lot easier in hexadecimal.

(This is the last table, I promise!!)

Binary	Hexadecimal
000000001 (1)	01
000000010 (2)	02
000000100 (3)	04
000001000 (4)	08
000010000 (5)	010
000100000 (6)	020
001000000 (7)	040
010000000 (8)	080
100000000 (9)	0100

As you can see, there's a bit of a pattern in the hexadecimal column. You might be thinking, there seems to be some sort of pattern of the numbers 1, 2, 4 and 8. And you would be right. Another detail you may notice is the zeros in front of the hexadecimal numbers (like 0100, rather than just 100). In SPHERE, that 0 tells the script "Hey, this number is HEX!" 0100 and 100 are very different numbers.

Let's say, for a SPHERE script, you need to set the 13th bit of a number (FLAGS, for example), you could write something like this:

SRC.FLAGS |= 8192

But would you really remember that 8192 is 2 to the 13th power? I didn't think so. What would be easier is to go down through your list in your head, until you reach the 13th number. (Remember, START AT ZERO when you're counting!)

01	02	04	08	010	020	040	080	0100	0200	0400	0800	01000	02000
2^0	2^1	2^2	2^3	2^4	2^5	2^6	2^7	2^8	2^9	2^10	2^11	2^12	2^13

And there you have it. The first 14 powers of two in hexademical.

SRC.FLAGS |= 02000

The above code is identical to the previous example. 8192 (decimal) is EQUAL to 02000 (hexadecimal)

8192 = 02000

You may be saying, "How do I know he's just not making all of this up?" Well, our wonderful friends at Microsoft have provided us with a nice tool that converters from decimal to hexadecimal to binary to octal (ANOTHER numbering system that is useless in SPHERE, so we will not deal with it). It's called the Calculator. You may find it by clicking your start button, going to Programs, then Accessories. Calculator should be sitting there looking pretty. Once in the calculator program, go to the View menu, and click Scientific. You'll see the display drastically change. To convert a number between numbering systems, simply click on the original system (Dec), type a number (8192), then click on the button for the other system (Hex). Automagically, Windows will convert your decimal number to hexadecimal. Stick a zero on the front, and SPHERE will be perfectly happy with it.

This is probably the hardest thing in all of SPHERE scripting to understand. Luckily, because of the next section, you won't have to deal with scary numbers most of the time. If I still have you at the end of this lesson, I know you're going to do great!

Onward to some SPHERE scripting!