Names For Hexidecimal Numbers

Jim   Wednesday, October 22, 2003, 07:48 GMT
Suppose we went hexidecimal. What would we call the numbers? The celts used base twenty perhaps we could import words from them. Aren't there traces left in French?
messire lavoisel   Wednesday, October 22, 2003, 12:35 GMT
I don't think there is any more trace of hexadecimal numbers' name than there is in English.

1: One, Un
2: Two, Deux
3: Three, Trois
4: Four, Quatre
5: Five, Cinq
6: Six, Six
7: Seven, Sept
8: Eight, Huit
9: Nine, Neuf
10: Ten, Dix

When it comes to numbers between 11 (included) and 19 (included), English sort of includes the word "ten" in their name from 13, only "ten" become "teen", while French clearly incorporate "Dix" , but wait until the number "17" to incorporate it.

11: Eleven, Onze
12: Twelve, Douze
13: Thirteen, Treize (here English begins to Incorporate a sort of "Ten")
14: Fourteen, Quatorze
15: Fifteen, Quinze
16: Sixteen, Seize
17: Seventeen, Dix-Sept (here French begins to incorporate "Dix")
18: Eighteen, Dix-Huit
19: Nineteen, Dix-Neuf

Then after, both languages are logical: they simply add the name of the unit at the end of the number

20: Twenty, Vingt
21: Twenty One, Vingt et Un
22: Twenty Two, Vingt Deux
23: Twenty Three, Vingt Trois

The only illogism which remains in French is the "et" before "un"

30: Thirty, Trente
31: Thrirty One, Trente ET Un (et is added before un)
32: Thirty Two, Trente deux (no "et" before the other name of unit)

I don't see any traces of hexadecimal name here.
Jim   Thursday, October 23, 2003, 08:10 GMT

I was thinking about the vigesimal system rather than the hexidecimal. I read and heard about these traces. What I think they meant is the names for 70 and 90.
Simon   Thursday, October 23, 2003, 08:33 GMT
Well, you notice how 11-16 all end in -ze. I think that's a left over of the Latin for ten, cf. Italian.

In Belgian French, they have Septante and Nonante (though not Huitante like the Swiss).
Simon   Thursday, October 23, 2003, 09:27 GMT
Ah but Jim, have you never heard of the word "score" (used as a number). It means 20: four score and three, 83
Jim   Friday, October 24, 2003, 04:42 GMT

You score 20 points on that one.

Though then there's dozen (it's got to be related to "douze"). Has anyone ever used a dozenal counting system?
Jim ... again   Friday, October 24, 2003, 04:58 GMT
Anyway, as we can see from Messire Lavoisel's post the numbers 11 to 19 in French are obviously formed by adding 1, 2, 3, ... 8 or 9 to 10. The case is the same for the numbers 13 to 19 (maybe 11 & 12 somehow) in English.

However, if society used base twenty, as it seems the celts did, surely they should have names for these numbers which had nothing to do with ten. Ten wouldn't have anything too special about it, it would just be half of twenty.

I'm curious as to what they were. If we went hexadecimal maybe we could make use of these names instead of "sixteen", "fifteen", "fourteen" and "thirteen". These "-teen" words put emphasis on ten but there'd be nothing special about ten in hexadecimal.

Otherwise, what would you call the hexadecimal numbers? Perhaps "1A9BF" would be "onety-ten thousand nine hundred and eleventy-fifteen." Hey, isn't "eleventy" already a word?
Simon   Friday, October 24, 2003, 08:17 GMT
Dozen comes from Douzaine meaning "about twelve or so". Cf. quinzaine (about fifteen), trentaine (about thirty). I think in French, they tend to use dixaine (about ten) where we use dozen.

I think in Welsh they have two sets of numbers. Hold on...
.   Sunday, October 26, 2003, 23:51 GMT
Jim   Monday, October 27, 2003, 01:09 GMT
Jim   Monday, October 27, 2003, 05:25 GMT
Ahh, where's Kevin when you need him? Anyway, here's a bit of stuff that I've managed to find on the web.

"Children who speak Welsh at home and at school may find it easier to acquire some aspects of numeracy than their English-speaking counterparts,"

From this site:
They say that this is because the system they usually use is simpler. This is the decimal one but there is a traditional vingesimal one too.

3. The traditional Welsh numbers between 10 and 20 are quite complicated, so for now, we'll use the simpler decimal system - though I have noted in brackets some of the traditional forms which you might like to learn.

11 - un deg un (un ar ddeg)
12 - un deg dau (deuddeg)
14 - un deg pedwar (un ar bymtheg)*
15 - un deg pump (pymtheg)
16 - un deg chwech (pedwar ar ddeg {m}, pedair ar ddeg {f})*
17 - un deg saith (dau ar bymtheg {m}, dwy ar bymtheg {f})*
18 - un deg wyth (deunaw)
19 - un deg naw (pedwar ar bymtheg {m}, pedair ar bymtheg {f})*
20 - dau ddeg (ugain)

This is from the site:

except for the bits with the * which came from

I'm guessing that {m} and {f} mean "male" and "female". So perhaps I'm on the right track with the notion that celtic languages have, or at least had, a vingesimal system.

But does it help? What I really want is words for 11 to 16 that are not just "this plus that" or "this minus that" kind of words. "Fifteen", for example is obvoiusly "five plus ten". What about "pymtheg"?

How did the Welsh come up with these words?
Da Frogg   Monday, October 27, 2003, 09:17 GMT
Here are the numbers in Breton, which is a Celtic language:
1 unan
2 daou / div
3 tri / teir
4 pevar / peder
5 pemp
6 c'hwec'h
7 seizh
8 eizh
9 nav
10 dek
11 unnek
12 daouzek
13 trizek
14 pevarzek
15 pemzek
16 c'hwezek
17 seitek
18 triwec'h
19 naontek
20 ugent

As you can see, the system is the same as in French, English... (11 is like 1 plus an suffix) except for 18 which seems to be an exception.

But! there is a trace of the ancient 20-based system:
30 is tregont
31 is unan ha tregont (one and thirty)

40 is daou-ugent (two twenty)
50 is hanter kant (half hundred)
60 is tri-ugent (three twenty)
70 is dek ha tri-ugent (ten and three twenty)
71 is unnek ha tri-ugent (eleven and three twenty)
79 is naontek ha tri-ugent (nineteen and three twenty)
80 is pevar-ugent (four twenty)
90 is dek a pevar-ugent (ten and four twenty)
100 is kant

As you can see, it's not always regular but it often goes by 20.
Simon   Monday, October 27, 2003, 09:52 GMT
Sorry, I forgot. I think the Welsh favour a decimal system now and the so called traditional alternatives didn't look all that special I must say.
Jim   Tuesday, October 28, 2003, 07:36 GMT
No, none too special, I've got to say. Only 20 has its own name: "ugain".

If 1 is "un" and 10 is "deg", it's not too hard to see how they came up with "un ar ddeg" for 11. Same for 12, which is "deuddeg", it's pretty obvious that this is just 2 + 10, "dau" is 2.

For some reason or other 13 is missing from the list. I'm grabbing it from
Also, I've noticed another mistake in my list above. I got 14 and 16 mixed up. The correct complete list should read like this:

11 - un deg un (un ar ddeg)
12 - un deg dau (deuddeg)
13 - un deg tri (tri ar ddeg {m}, tair ar ddeg {f})
14 - un deg pedwar (pedwar ar ddeg {m}, pedair ar ddeg {f})
15 - un deg pump (pymtheg)
16 - un deg chwech (un ar bymtheg)
17 - un deg saith (dau ar bymtheg {m}, dwy ar bymtheg {f})
18 - un deg wyth (deunaw)
19 - un deg naw (pedwar ar bymtheg {m}, pedair ar bymtheg {f})
20 - dau ddeg (ugain)

But I'm not finding anything ground shattering when I look at 13 and 14. It seems that in the traditional system the numbers 11, 12, 13 & 14 are just 1 + 10, 2 + 10, 3 +10 & 4 +10. Whereas in the decimal system they are 10 + 1, 10 +2, 10 + 3 and 10 + 4. Either way they haven't been given their own names like the numbers 1 to 10 have.

Of course, someone might want to point out that "d" and "dd" are pronounced differently in Welsh but still you can see that they are related. The connexion between "three" and "thirteen" is obvious even though "ree" and "ir" are quite different.

Things get interesting when we get to 15. It seems that it might have it's own name, "pymtheg" rather than "pump ar ddeg". But my guess is that "pymtheg" is just short for "pump ar ddeg".

In Welsh "dd" is pronounced like the "th" in "that" and "th" is pronounced like the "th" in "thing". So "dd" and "th" are related, the only difference is that one is voiced and the other is not.

Take "pump ar ddeg" change the first vowel from "u" to "y", drop the "p" and the "ar" then devoice the "dd" and you get "pymtheg". Perhaps the voicelessness of the dropped "p" carried over to the "dd".

It's a different story with 16 and 17, "un ar bymtheg" and "dau ar bymtheg"/"dwy ar bymtheg". It's pretty clear that these are 1 + 15 and 2 +15. The same goes for 19. You can see that "pedwar ar bymtheg"/"pedair ar bymtheg" is 4 + 15. All that's going on is the "p" in "pymtheg" gets voiced.

We've got something new with 18, "deunaw", as you can see, means 2 x 9. Like Breton 18 is an odd one out in Welsh. What's interesting, though, is that in Breton 18 is "triwec'h", this is 3 x 6 rather than the Welsh 2 x 9.

In Breton too, only twenty has its own name, "ugent". Breton and Welsh are very similar. I suspect Welsh has traces of the base twenty system in the names of numbers higher than 20 too like Breton and French.