h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Wouldn't base 2 be 1010, Prof?

G7

*Matina notices lamb and rolls directly over to hook. She unhooks the lamb and takes it to the kitchen. Cooking noises ensue*

Wow, a double-posting unau - ladies and gentlemen - for the very first time in the history of h2g2 - at least I think so...

Citizens? I'd happily settle with humans, but OK... *shrugs*

No, really, 1023.

10 fingers and thumbs, OK? Now, we go up in powers of two, like so.
1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 = 1023. Tada!

Base 2 is binary, for all those non-techies out there.
Our decimal system is of course base 10.

*sweet smile*

And now Prof, would you please explain to us exactly how you end up with that answer only using your fingers?

I do have a calculator, actually. It's nearly 15 years old, solar powered, and it converts between decimal, hex and binary. Does calculations in all three radices. Um, I think it does octal as well, but I have never had a use for that radix.

I have a computer. I do not know how to use most advanced functions on a calc anyway so I just use my compy to do the simple stuff. Anything else I leave to smarter people.

Did I say how badly I hate math?

My calculator needs a new battery. That's why I just use one on the computer now. Any other sums can be done in my head or with a pencil and paper

My other calculator does all four conversions too.

Right, OK. In binary, let's say each of your fingers can represent two states, 0 and 1. All fingers down is 0 and all up is 1023.
So that's: 0000000000 and 1111111111.
Each finger represents a column. In our decimal system we have units, tens, hundreds, thousands, etc. In binary we have units, twos, fours, eights, sixteens, etc. Hence, our hands are laid out thusly:

| 512 | 256 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

So, a value of 1 in the '1' column would give us, uh, one one. A value of 1 in the '2' column would give us one two. A value of 1 in the '2' column and a 1 in the '1' column would give us one two and one one, or three.
I'll leave you to work out how to get a value of 10.

The reason I used only binary as an example is because our fingers can only have two states (unless you want to be really clever and only have them up by defined amounts ). If each finger could show ten states like our decimal system then we could count up to 9999999999.
And hex! Woah! I never realised counting on fingers was so interesting!

*gives up*

Has anyone here heard the Tom Lehrer song "New Math"?

I have indeed and it was just running through my head.

Binary cannot have any numeral over a 1 though, Prof. this was my problem. If you count to ten (base 10) in binary, you go: 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010. That's where I got my 1010.

G7

*refuses to do math when not neccissary*

Each finger has two states though. And as each finger has an increasing value (going up by powers of two), we get some prety big numbers.
Oh, and I tried to work out the largest hex value we can represent with out fingers (FFFFFFFFFF), but the calculator screen wasn't big enough.
It's 16^10 though, if anyone else wants to try.

/* tin can speaks */
I am very upset at Chris for making me think in binary. Dang! He goes straight for my weakness.

Lil, I'm one of the ones who hasn't done any homework.

Binary is something I ahve to think is every so often. I also count things like eggs starting at 0. It annoys my room mate when he assists me in the kitchen.

"I bought a dozen eggs today. Look, 11!"

G7

Got it, Prof. Sorry 'bout that.

G7