Episode -2: 0xE2? Wtf? Addendum to the MySQL series

Hello, human. You probably learned to count to ten. You probably use 0 to 9 to write numbers.

That’s great! But there are other ways to do things.

Computers, you’ve probably heard, store everything as ones and zeros. Fortunately, most of the time modern programmers don’t have to care about this. But character encodings are one of those times when we get pretty close. But don’t worry! You can totally comprehend this.

So computers learn to count to 2, using only 0 and 1. “Wait, what?” you may ask, “How do you count to 2 without a, you know, a ‘2’?” Great question! But consider: you count to ten without a character representing ten! You just put a 1 in the “tens” column, and a 0 in the “ones” column.

Computers do something similar, but instead of having a tens column, they have a “twos” column. So you start counting at one, “1”, which is followed by two, “10”. Only, in binary, we know that “10” means we have one 2 and zero 1s. So “10”, in binary land, means 2! Crazy, right? Can you think of how you’d write three in binary?

The thing is, writing binary numbers out as a bunch of ones and zeros is terribly painful for humans. And unfortunately, converting binary numbers to decimal is a little bit of a bummer sometimes, because math. Specifically, you can’t double 2 an even number of times to arrive at 10. (2 * 2 = 4, * 2 = 8, * 2 = 16).

Writing binary as base 16 numbers is actually really nice. At least, the brilliant minds that were programming back when computers first existed all agreed, and we’ve all gone on learning it.

Base 16 means you have a ones column, and then you have a sixteens column. That’s right! And just as base 2 (binary) requires 2 characters to write out all the numbers (0 and 1) and base 10 requires 10 (0 to 9), base 16 requires16. But we don’t have single characters for numbers bigger than 9. The solution, said brilliant programmers decided, is to use A to F. “A” in base 16 means 10, on up to “F” meaning 15. (If you’re wondering what happened to the number 16 and why we didn’t include G, think again about how we write ten in base ten).

Base 16 is also called “hexadecimal”, which people often shorten to “hex” to save time. When you want to write hex numbers but don’t want to give a big long explanation beforehand (“Watch out, everyone, this looks like ten but is actually sixteen because it’s hexadecimal!”), you can prefix your number with “0x”.

So! 0xE2 means “the hexadecimal number E2”. “E2” means you have E (that is, 14) sixteens, and 2 ones. So this number in familiar Decimal notation would be 14*16 + 2 = 226. Written out in binary it would be… friggin’ annoying. 1110 0010. (A string of 8 zeros or ones (that is, a string of 8 bits) is called a byte.)

Now, you’re correct, these are just numbers. They’re not letters. 0xE2 does, in a very real, mathy sense, mean 226. But it does not mean “â” (or “ç” or “Z” or “∆”). The only thing that makes it mean some-character is that all we humans agree on what letter it ought to stand for. We map numbers, like 226, to letters. And we call these mappings “encodings”.

Numbers smaller than 127 map to the same characters in basically all encodings, and are called ASCII. For numbers bigger than that, you must know what encoding you’re working with. Because everyone in the world used to use different ones.

Here’s what we call Latin1. And if you’re curious to keep learning more, I highly recommend Joel Spolsky’s article on Unicode, which is where I first learned about the terrible, ever-present world of encodings.

 
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