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# TerraGraphics

I'm going to teach you all about hexadecimal right now but first we have to look at numbers in general. It's going to sound trivial at first, but please bare with me. I have to establish a vocabulary.

Every system of writing numbers works by using a finite set of symbols to express an infinite set of numbers. Being smart enough to count on both hands, we came up with 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 to express the first few numeric values. There are ten of these symbols, so we call our numbers base ten numbers or decimal numbers. Each symbol represents a unique value enabling us to write any of the first ten values using a single symbol. The first value that we can't write with a single symbol (the one after 9) just happens to be the one our system is based on. So we make a place to the left of where we've been writing our symbols and write a 1 there meaning we have one amount of our base plus whatever we write in the original place. We call this a place system. The first (rightmost place) just contains one of our symbols to indicate how many. The second place (to the left of the first one) tells how many of our number base quantities to add in. E.g., 24 means two sets of our number base plus four more.

I read that there are tribes of people who have been isolated on islands for approximately forever, and some of these people just count on one hand. They have only 5 symbols in their number system. I don't know what they look like but I'll guess they are 0, 1, 2, 3, and 4. I'll call this a base five system. Now, lets suppose these folks invented a place system as we did. The first value that they can't write with a single symbol (the one after 4) just happens to be the one their system is based on. So they make a place to the left of where they've been writing their symbols and write a 1 there meaning they have one amount of their base plus whatever they write in the original place. They call it a place system. The first (rightmost place) just contains one of their symbols to indicate how many. The second place (to the left of the first one) tells how many of their number base quantities to add in. E.g., 24 means two sets of their number base plus four more.

Consider this: When we write 24, we mean: xxxxxxxxxx xxxxxxxxxx xxxx
When those islanders write 24, they mean: xxxxx xxxxx xxxx

Now there's just one more thing to consider. When the number system described above (either one) gets to the first one it can't express with two symbols (after 99 or 44) the next value just happens to be the base squared and using another place to the left solves the problem again and we write 100. Then, after 999 or 444 we'll get 1000 in either system.

If there is anything above, you don't completely and thoroughly understand, go over it until it's so obvious that it's boring. Try writing some base five numbers and figuring out what they mean. If you want to have some real fun, try adding a few of them and see how the carries work just like they do in base ten. If you work at it a while, you'll find you can convert any number from one system to the other.

Guess what? You're done. You understand hexadecimal. It has sixteen symbols which are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.
When you write 24, you mean: xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxx

Want to know octal? The eight symbols are 0, 1, 2, 3, 4, 5, 6, and 7.
When you write 24, you mean: xxxxxxxx xxxxxxxx xxxx

Okay, what about binary? The two symbols are 0 and 1. You can't write 24 but when you write 11, you mean: xx x
That's right - same as the other bases. The first value that we can't write with a single symbol (the one after 1) just happens to be the one our system is based on. So we make a place to the left of where we've been writing our symbols and write a 1 there meaning we have one amount of our base plus whatever we write in the original place. Also, just like the others, we run out of two digit numbers when we reach the base squared and we write: 100
When you write 111, you mean: xxxx xx x
If you came from an island where they use binary, you might say, "There are 10 kinds of people in the world - those who understand binary and those who don't."

If you put a dozen eggs in an egg carton and give them to your friend who lives on base five island he'll say, "Wow! There are 22 eggs here." Then, his octal friend will say, "No, there are 14". Then they'll go see their hexadecimal friend who'll say, "You are both wrong. There are only C eggs in here." But, their binary friend will say, "You are all making it so complicated. The simple fact is, there are 1100 eggs in this box.