## A Conversation for Number Systems

### Minor "nit picks"

Ausnahmsweise, wie üblich (Consistently inconsistent) Started conversation Aug 30, 2001

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

### Minor "nit picks"

beeline Posted Sep 24, 2001

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!

### Minor "nit picks"

Max C Posted Oct 8, 2001

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.

### Minor "nit picks"

Ausnahmsweise, wie üblich (Consistently inconsistent) Posted Oct 8, 2001

...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".

### Minor "nit picks"

Ketman Posted Oct 9, 2001

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.

### Minor "nit picks"

Max C Posted Oct 9, 2001

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

### Minor "nit picks"

beeline Posted Oct 9, 2001

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

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### Minor "nit picks"

- 1: Ausnahmsweise, wie üblich (Consistently inconsistent) (Aug 30, 2001)
- 2: Ausnahmsweise, wie üblich (Consistently inconsistent) (Sep 24, 2001)
- 3: beeline (Sep 24, 2001)
- 4: Max C (Oct 8, 2001)
- 5: Ausnahmsweise, wie üblich (Consistently inconsistent) (Oct 8, 2001)
- 6: Ketman (Oct 9, 2001)
- 7: Max C (Oct 9, 2001)
- 8: beeline (Oct 9, 2001)

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