Even with the proliferation of computers everywhere, not everyone knows exactly what binary means and what the hoopla is all about. Several FAQs on PokéFAQs refer to binary numbers and rely on the player knowing a certain amount about the binary system. This document will cover the basics necessary to understand what binary notation is, how it is important, and how to bridge the gap between binary and the real world.

I'll be honest with you. You don't need to know binary in order to enjoy Pokémon. You can live a very happy life and never understand the inner-workings of base-2 number systems. Probably. But there are Pokémaniacs out there who live and breathe this stuff. They analyze their Pokémon's stats with an intensity Hannibal the Cannibal would find unsettling. They dream at night of randy shiny Dittos and max-stat Tyranitars. When they can't sleep they count Ampharos in their heads. They skip Disneyland with the family so they can work on the happiness factor of their Golbat. It is for these people that understanding of binary is useful.

Just don't forget, folks, Magic Mountain is fun too!

Introduction

Pokémon is, among other things, a video game and as such our interface to the game is via a computer—in this case, the Nintendo Gameboy™. Yes, it is a game console but at the heart of the machine is a computer, very much like the PC that you are probably viewing this document on. The microprocessors may be different, memory capacity may be different, but it is still a computer.

The Gameboy hand-held computer runs programs just as any other computer does. But it has a specialized function—the programs it runs are games. Be that as it may, these games are still programs. Programs are simply lists of instructions for the computer to execute, one right after the other.

The programs that it runs, the instructions that get executed, are all stored as numbers. You may ask yourself "Numbers like 5, 12, and 144?". Well, yes and no. It does use numbers like those and many others, but it is the number system that is different than what humans use.

You have probably heard that computers use things like bits and bytes. This is true and in the following discussion we will discuss just exactly what these bits and bytes are and how to use them.

Number Systems

The smoothest way to introduce a new number system is actually to go back in our minds to around fourth or fifth grade and refresh our memories about how our own number system works. If you happen to be currently in the fourth or fifth grade, the following may not make complete sense, but give it a shot if you want a challenge.

Base 10

The root of a number system is it's base. Pretty aptly named wouldn't you say?

The base of a number system is simply it's number of unique digits within it.

Our own number system that we use day-in and day-out is base 10. That is to say, there are ten individual, unique digits that make up our number system. These numerals are: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. With these ten digits we can represent any rational number in the universe.

You may ask "But what about twelve, ninety-nine, or a hundred and six? Where do these come from?" As you will see, these and all other numbers are just extensions of those ten unique digits.

Using these digits, it is easy to see the numbers 0 through 9. Alice has six apples. You know what six means and therefore know how many apples she has. But what if she has 12 apples?

This is where the base in base-10 comes from. Recall that 12 is simply 10 + 2. Also recall that the numeral 1 located where it is in the number twelve really means ten (hence the name tens-place). Ten plus two equals 12. No big deal.

What about 32? The exact same thing applies. The three simply means you have three "tens" plus two, or thirty-two. Clear as Pokémon Crystal.

Lets take it a step further. How about 563? The 5 is located in the hundreds-place and means that you have five sets of a hundred. A hundred means ten sets of ten. The 6 located in the tens-place indicates six sets of ten, and the 3 is simply three (three sets of one if you will). So if you wanted to be long-winded, you could say "five hundred and sixty-three is equal to five sets of ten sets of ten plus six sets of ten plus three." Whew. You can see it's much easier to say 563 instead of that huge mouthful! If we had to talk like that, no-one would get any math done and we'd all live in caves, wear animal skins, and eat dirt.

It is the concept of this number system that is important. Take this thought and generalize it a moment. Here is another way of looking at this.

Figure 1: How base-10 numbers are represented