Deena - you hit it on the head. Oh boy did you!!!

I don't know what you mean by binary code.

I do know what you mean by binary code.

(No, I don't. I just wanted to go for the true binary X-post.)

Um. Maybe I'm referring to it incorrectly. But since I don't know anything about it, I don't know how I should be referring to it. So far the mathiest people in this thread don't know what I mean, and I don't know how to articulate what I mean.

If you were explaining the binary....system (? is that a better term?) to a retarded 3-year-old lemur, how would you explain it???

Or, what's the story with all the 0s and 1s? How does it work? How does one count with only 0s and 1s? How is that used in relation to computer programming? Or, *is* it used in relation to computer programming? How do a bunch of 0s and 1s make my iTunes work?

Steph, do you understand bases? Like the principle of base ten (decimal) vs. base eight?

Steph, do you understand bases? Like the principle of base 10 (decimal) vs. base 8?

Um. Someone explained base 8 recently -- I can't remember which thread -- and by "recently," I mean "in the past few or 6 months" -- and I sort of grasped the idea, but not really.

Base 10 is just....the numbering system that we common non-mathy folk use in everyday life, right? Because I get that. That's about the only math I get.

Binary is just counting when the largest digit you can use is 1.

So:

Regular Number   Binary Number
         0                     0
         1                     1
         2                    10
         3                    11
         4                   100
         5                   101
         6                   110
         etc...

why is a^p = a in Z sub p when p is prime?

That's a direct consequence of Fermat's Little Theorem. Have you learned that yet?

Also, if you divide f(x) by (x-a), why is the remainder always f(a)?

Hmm. I'm not sure about that one. You're assuming that f(x) is a polynomial? You can probably do something with the division algorithm, but I'm not sure exactly what.

Okay, but I don't understand that chart. How does 6 in normal numbers = 110 in binary?

Some computer calculator programs can convert to and from binary. I forget if the one that comes with OS X does that, but the Win XP does.

I had a tag recently that said "There are 10 types of people in the world, those who understand binary and those who don't." Gud's table explains the joke.

Also, if you divide f(x) by (x-a), why is the remainder always f(a)?

*This* is an understandable question, but "what up with binary code?" ISN'T? You mathy types are confusing.