How do you say $10$ when it's in binary?

Question

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?

Answer 1

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."

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The confusion here reminds me of this T-Shirt:

Answer 2

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.

Answer 3

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.

Answer 4

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, just as when it's in decimal, $10$ is ten.

Of course, when read as a string of numerals, it is perfectly valid to read $10$ as "one-zero", no matter what base it is in.

Answer 5

We had a pretty heated discussion with my coworkers on this subject and here is my argument.

As part 1, we have in any base :

• 0 and 1
• if exists, 2 is the successor of 1, noted as 2 = succ(1)
• if exists, 3 = succ(2)
• ...
• if exists, 9 = succ(8)
• if exists, A = succ(9)
• if exists, B = succ(A)
• ...

Those numbers have a unique name. It's not confusing.

As part 2, we have in any base :

For a base X (base 2, base 10, base 8, ...), 10 is the successor of X - 1. As :

• in base 10, 10 = succ(9)
• in base 8, 10 = succ(7)
• in base 2, 10 = succ(1)

10 in any base have the same meaning (not value) : changing the order of magnitude.

As part 3,
Counter-argument to "ten is the successor of nine so it can't be the successor of one".

It means either :

• "A" should be called "ten" and it's even more confusing
• "ten" is a word with meaning only in base 10. So the base 10 is not any base without any mathematical argument but "because I said so".

As part 4,
In natural language :

• the single digit numbers can't be mistaken because of the hypothesis "if exists"
• multiple digits can leads to confusion when talking about multiple bases.

But we have a notation to specify the base of a number (which can be found in any article such as this one) :

The base should be specified as follow : (X)y

Te be understood orally, we have to specify the base ("X, base y") with base 10 as default ("X" means "X base 10").

In conclusion,
10, in any base, should be called "ten" because it means the same thing in any base.
In case of possible confusion, we should specify the base as in "ten, base two".
The same argument applies to 11, 1000 and so on and so forth.