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

Hi "WhoAmI",

Just a couple of little things.
You added something about logic gates. Unfortunately there are tri-state logic gates. I wonder if this might confuse the reader.

I had deliberately spaced (justified) the binary representation so the reader could see how it was growing
___0
___1
__10
__11
_100

etc. I wonder if you could keep it that way, unless there's a technical reason for doing it otherwise.


You refer to A as ten, B as twelve, etc. These are base ten concepts. I think ther reader should try to forget about those and just know that after 9, comes A, then B... etc., depending on the current number scheme.

Hope you don't mind me butting in

Awu

Hi,
it's the pest again
trueencryption should be true encryption.
Awu

Hi Ausnahmsweise,

Fixed those - thanks. That was quite a subtle point about 11, 12, 13, etc, as our writing guidelines say to use numerals for anything after 10, but you're right - those numerals are base-10 oriented by their very writing! I'll edit appropriately.

Well spotted!

Actually, "ten" is not a base ten concept. The number ten is written in different ways in different bases, but it is always the number ten: the concept of the number of fingers I have.

...but if I was counting in, say hexadecimal, I wouldn't say "ten" out loud after saying "nine". That's what I meant. I would say "A". When I got through A, B, C, D, E and F and reached 10, I might call that "ten hex".

I think it's okay to say ten out loud. It's also okay to write "ten". What you don't do is write "10". I can say "two-nought" or I can say "thirty-two"; either way I mean four times eight. There is no ambiguity.

I think Ketman explains it well. "Ten hex" is really "A", although some people would think that it meant sixteen ("10" written in hex), so it's probably best avoided.

The key here is the difference between a number (ten) and a representation of that number (10, 1010, A, whatever). This becomes important in situations where there is more than representation for a number in the same base. For example in decimal, "0.999... recurring" represents precisely the same number as "1.0" does. The number one is a concept which we all understand, and it exists independently of bases. I've written more boring stuff about this in the "Uniqueness of representation" thread.

M

Check http://www.bbc.co.uk/h2g2/guide/A592553 for the proof.