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.

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.

Um. Okay.

Steph, binary counting is based on saying that every number can be expressed as the sum of powers of 2: 1, 2, 4, 8, 16, 32, 64, etc. The first digit (first on the right) is how many ones there are -- so every odd number will have a 1 there, and every even number will have a 0 there. The next digit is how many 2s there are. So 2 is 10, 3 is 11, since it's 2+1. And so on.

So, 9 = 8+1, so in binary it's 101. 10 = 8+2, so in binary it's 110. 19 = 16+2+1, so it's 1011. Etc.

Let's use eggs instead.

Now Pe R. Son uses a 10-egg egg crate, but the town idiot Comp U. Ter uses a 2-egg egg crate instead. So if you have 3 eggs then P. Son doesn't have enough eggs to fill a crate so he says he has 3 eggs. C. Ter says he has one crate and 1 egg.

So for Pe R. Son - No crates and 3 eggs or "3" for short.

For Comp U. Ter - 1 crate and 1 egg or "11" for short.

Binary translator: [link]

Pretty sure it was tommyrot who posted that originally. But I don't if it's helpful to you in referencing binary in text.

Teppy, in regular numbers, when you get to 9, you're run out of numbers and have to add a place to say that you've hit 10. each time you hit 10 you increase that digit (in the tens place) by 1, until you run out of digits, and then you add the Hundreds place.

Binary does that same thing, only you run out much faster, as you only have 2 options for digits to put in a place, 0 and 1. So, rather than 10 (ten), meaning 1 ten and 0 units, you have 1 two and 0 singles. 100 would be 1 four, 0 twos, and 0 singles

How does 6 in normal numbers = 110 in binary?

Say you have 143. 143 in regular #s = 1*10^2 + 4*10^1 + 3*10^0
or 1 x 10^2 + 4*10 + 3

Now say you have 110 in binary. That = 1*2^2 + 1*2^1 + 0*1^0
or 2^2 + 2^1 + 0*1

Steph, 100 is four, 10 is two, so 110 is 6. That link I gave looks pretty good -- you might want to give it a try. I was confused by your original question because there's the binary numbering system -- which is just like counting, only instead of having a units place, tens place, hundreds, etc. you have a units place, twos place, fours, etc. -- and then there's using binary numbers for coding because then you can write everything in terms of on or off.

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

THANK YOU! I knew it was something simple, but I couldn't find what it was! So x^p+a is always factorable in Zsubp because (x^p+a) = (x+a)^p, is what I'm putting, because the intermediate coefficients are always multiples of p. The other thing should totally use the division algorithm, only I can't figure out why either.

(I knew once we figured out what was being asked, it would be a veritable orgy of binary-explaining.)