🚀 go-pugleaf

Barb Knox wrote:
> In article <46e82fc7$0$4039$9a566e8b@news.aliant.net>,
>  "Dugie" <d_fren@DOTSPAMhotmail.com> wrote:
> 
>> Hi,
>>
>> I'm obviously not a mathematician. :) But I'm fascinated by some aspects of
>> numbers.
>>
>> One question: how are numbers in non 10-based systems pronounced, as  when
>> counting?
>>
>> Example - "thirteen" (13) in base 10 makes sense, but
>>               - how is D (13 in hex) pronounced?
> 
> "dee"
> 
> And clearly, '10' in hex is not pronounced "ten"; say "one-zero" instead.
> 
>> Thanks,
>> -Dugie
> 
> You're welcome.
> 
Your example is incorrect, too.
"how  is D (13 in hex) pronounced"
should have been
"how  is D (13 is the decimal equivalent) pronounced"

13 in hex is "one three" or 19 base 10 ( or nineteen)

When you start looking at non-decimal systems (such as hexadecimal), try to 
imagine the characters represented by the notation as just a bunch of squiggles 
that represent the base count

Take octal

1 2 3 4 5 6 7 and a "0" for positional shifts

These are the only allowable squiggles in this system.
They look like numbers from the decimal system, so just pronounce them like you 
would in a decimal system

In the decimal system, you have ten squiggles. They look like

1 2 3 4 5 6 7 8 9 and again a "0" for positional shifts

In a hexadecimal system, these squiggles look amazingly similar to the decimal 
system, with a few alphabetic characters tossed in. i.e.

1 2 3 4 5 6 7 8 9 A B C D E F G  (plus "0")
phonetically
"wun tu three for five six seven ait nine ai bee cee dee eee ef gee"

How else would you say the letter "D"  but "dee"

Remember, it's only a one character representation of the thirteenth squiggle in 
a sixteen digit system. It just happens to look like an alphabetic "D" and is 
pronounced the same way.

It's a pity really, that the hexadecimal system wasn't set up with a random 
group of squiggles from the alphabet, like

1 2 3 4 5 6 7 8 9 Z X C V B N M

or even

1 2 3 4 5 6 7 8 9 < > ^ ~ ` | /

but that would mean we'd then have to use other symbols to represent "less 
than", "greater than", "power" etc when applied to maths, so... use the "KISS" 
(keep it simple, stupid) principle, and just use the first six letters of the 
alphabet to represent those extra squiggles.

After all, EVERYBODY knows "A" is before "B" is before "C" is before "D" is 
before "E"  is before "F" is before "G", so it pays to use them IN THAT ORDER to 
represent the six squiggles after the first nine in a hex system

The same principle applies to ANY numeric system. If there are some characters 
that look like they are part of the alphabet, believe me, they aint. They are 
just squiggles that represent NUMBERS.

It's a mind-set thing, really. All your years in primary schooling is based 
around a decimal numbering system, and the alphabet to express language. They 
don't mix with most people. Once you get that mind-set past the idea that 
alphabet symbols aren't part of the alphabet when they're in a numeric system, 
then you begin to "read" in hex.

I  got to that point myself, where just looking at a string of hex notation 
makes sense. It became fun to read basic machine code faster than other 
students, but I never got as far as some of the really, really bright ones, who 
could "see" where a mistakes occurred in programming machine code, just by 
looking through the ticker tapes (gee, that dates me just a bit).

It's like braille or Morse code (or even a foreign language), once you learn it, 
you stop "converting" in your mind, and it just is

I hope I've been of help with non-decimal systems.

Argusy