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I always assumed $10$ was pronounced "ten" regardless of whether it's binary, decimal, or another system, just like how 5 is "five" in all systems that the digit exists exists. But someone told me that, if it's not base-10, it should be pronounced "one-zero", and that "ten" is the name of the number, not the ordered group of digits. I see no reason why it should, as taking that logic to hexadecimal, a should be called "ten", b "eleven" and so on. To me, that sounds like it would create more confusion. However, I have nothing to support (or refute) my view (neither does he, so far).

So, what is it, really? Or is it personal preference?

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If in hex you call 10 "ten", what would you call 1F? –  Rahul Sep 19 '11 at 10:17
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I would pronounce it 'two'. In order to remove potential for ambiguity, names for numbers should refer to their value and not to their representation in a particular notation (even though we derived the names from our experience with a base-10 system). Therefore '10' in binary notation is 'two' and '10' in decimal notation is 'ten' and '10' in hexadecimal is 'sixteen'. Similarly 'a' in hex is 'ten', 'b' is 'eleven' et cetera, just as you guessed. To fully remove ambiguity you can subscript the notation with the base, as in '$10_{10}$' for ten (in decimal) and '$11_2$' for 'three' (in binary). –  Chris Taylor Sep 19 '11 at 10:27
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@Rahul, i propose fteen :) –  Mike Sep 19 '11 at 10:27
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See the Schoolhouse Rock video on "Little Twelvetoes", and how he counts. youtube.com/watch?v=Myu_5eNdSJo&hd=1 –  GEdgar Sep 19 '11 at 14:06
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@Rahul: In hex, you call $10$ "sixteen". In hex, $\mathrm{A}$ is "ten". $1\mathrm{F}$ is "thirty one" or "one-F base sixteen". –  robjohn Sep 19 '11 at 20:49
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4 Answers 4

up vote 15 down vote accepted

As a professor who faces this issue every time I teach (cryptography and algorithms both tend to run into non-decimal bases), I have the following policy:

  • If decimal, just say the number (with the word "decimal" if we're mixing contexts)
  • If any other base, read the digits and say the name of the base

So I might say, "therefore the answer is one-zero-one binary, or 5 decimal."

I would never call 10 hex "ten". Nor would I call 10 binary "two."


The confusion here reminds me of this T-Shirt:

enter image description here

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That joke could be one of the reasons I thought about it the way I did in my question. To say the joke out loud, you basically have to call it "ten". But beyond that, it seems my view is the wrong (or at least, less popular) one. –  AlbeyAmakiir Sep 19 '11 at 23:04
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@Albey: The joke doesn't work so well when said out loud; I think it's doomed to be a T-Shirt (or bumper-sticker or email sig, etc) identifying the wearer as a huge nerd. :) –  Fixee Sep 20 '11 at 0:12
    
It works perfectly when said out loud. You pronounce it the normal way it would be pronounced -- "one zero". –  David Schwartz Dec 21 '11 at 23:08
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"There are 10 types of people: those who understand ternary, those who don't, and those confuse it with binary". And so on, extending it to other bases. :-) Because of course, every base is base 10. –  ShreevatsaR Dec 22 '11 at 8:06
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@DavidSchwartz: If you say it out loud as "one zero", then it doesn't "work perfectly" in the sense that it's no longer a joke, because it's not as unexpected. The "joke" in the written version is that you naturally read "10" as "ten", and then only when you encounter the word "binary" (or reach the end of the sentence) do you to reinterpret what "10" meant. With "one zero", the interpretation is held in abeyance until explanation is given... a listener doesn't automatically interpret "one zero" as "ten" the way a reader interprets "10" as "ten". –  ShreevatsaR Dec 22 '11 at 10:09
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one plus one is two in any base, whether it is binary or decimal. ** is two asterisks, not "ten base two". "binary ten" or "ten base two" would be the binary representation of ten, which is $1010_{two}$, not $10_{two}$ which is two.

$10$ when it's in binary is two.

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If you are thinking of these numbers as just strings of digits then, when speaking, I would just list the digits. Otherwise I would say "binary ten." If, after some conversation in which every number mentioned is a binary number I would suggest we simply drop the word "binary." If this is written I would use the notation Chris Taylor describes.

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May I request you change the phrase "binary 10" to use only letters and not digits? –  MartianInvader Sep 19 '11 at 19:59
    
Made the change –  Jay Sep 19 '11 at 20:02
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I'd say "two"... A professor at my university said that you should call it with its actual "value", so 10 in binary is "two" in value. "Ten" means 10 units (in decimal), or 1010 in binary. Anyway I think it's just his own opinion.

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