4
$\begingroup$

Using decimal representation for numbers,

we read 10 as ten (not as one, zero) we read 1011 as one thousand eleven (not as one, zero, one, one digit by digit).

But using binary representation, how 10 and 1011 should be read? Is digit by digit the only way?

$\endgroup$
5
  • 1
    $\begingroup$ Actually, some language do read decimal numbers in a way that is closer to digit by digit. We might be happier (English-speakers) if we read 11 as onety-one. $\endgroup$
    – Sue VanHattum
    Jun 23, 2023 at 16:31
  • $\begingroup$ @Sue VanHattum Which lanaguages do so? $\endgroup$ Jun 24, 2023 at 18:29
  • 1
    $\begingroup$ I googled 'how each language says numbers, and found this. "Contrast this with Mandarin Chinese, where the relationship between the tens and the units is very clear. Here, 92 is written jiǔ shí èr, which translates as “nine ten two”. Japanese and Korean also use similar conventions, where larger numbers are created by compounding the names for smaller ones. Psychologists call systems like these “transparent”, where there is an obvious and consistent link between numbers and their names." bbc.com/future/article/… $\endgroup$
    – Sue VanHattum
    Jun 24, 2023 at 19:22
  • 1
    $\begingroup$ @SueVanHattum Another interesting point re: number names is that, in Chinese, the single-digit numbers (as well as the powers of 10 through 10^4) all have one-syllable names, and this confers a short-term memory advantage. $\endgroup$ Jun 25, 2023 at 0:27
  • $\begingroup$ Related: academia.stackexchange.com/q/165526/64 and academia.stackexchange.com/q/197524/64 $\endgroup$
    – JRN
    Jun 25, 2023 at 13:34

2 Answers 2

7
$\begingroup$

In any discussion of numeral systems, I think it’s important to distinguish between numbers and numerals.

  • The number whose name is “ten” is a mathematical object.
  • The numeral "10" is a symbol.

When a symbol is used to signify an object or idea, we often read it by saying the name of the signified. For example, I might read a sign with the symbol "🚭" as "no smoking." Similarly, without any additional context, I might read the sentence "10 is an even number" as "ten is an even number."

Following this method, if the context is that we are working in base-2, then it would make sense to read the sentence "10 is an even number" as "two is an even number."

When we want to refer to a symbol itself (often indicated using quotation marks around the symbol), then we often read the name of the symbol, or we describe the symbol. For example, I might read the sentence "'10' has two digits" as "the numeral one-zero has two digits."

There is another method of reading that is specific to numerals used in place value systems. Its purpose is primarily pedagogical. From left to right, we read each digit, followed by its corresponding place value. I've often heard this called "expanded form." For example, in the context of base-2, I might read "10" as "one two and zero ones."

Others can probably suggest even more methods of reading numerals. To summarize, here are the three I've described, applied to the numeral "1011" in the context of base-2.

  • Read the name of the number: "eleven."
  • Describe the symbol: "one-zero-one-one."
  • Read the number in expanded form: "one eight, zero fours, one two, and one one."
$\endgroup$
2
  • $\begingroup$ The first method doesn't work except for very small numbers or very gifted students. I think the second one is the most common but I'll consider the last one in the future - I've never thought about this way so far! $\endgroup$
    – Jasper
    Jun 27, 2023 at 7:16
  • $\begingroup$ @Jasper I think it all depends on purpose. The first method deemphasizes the numeral itself, which is typically not what you want to do if your purpose is teaching about a numeral system. But it’s appropriate if your purpose is efficiently communicating a number. This is especially common with Roman numerals, e.g. a newscaster reading “Super Bowl LVI” as “super bowl fifty-six.” But binary is not very suited to efficient human communication of numbers, so I agree that you would rarely be in a situation where you would want to use the first method. $\endgroup$ Jun 28, 2023 at 17:31
-4
$\begingroup$

There is not solid standardization for this terminology. But one convention is this

\begin{array}{|c|c|c|} \hline \text{1} & \text{one} & \text{bit} \\ \hline \text{10} & \text{two} & \text{crumb} \\ \hline \text{100} & \text{four} & \text{nibble} \\ \hline \text{1000}& \text{eight} & \text{byte} \\ \hline \text{10000}& \text{sixteen} & \text {word}\\ \hline \text{100000}& \text{thirty-two} & \text {dword}\\ \hline \end{array}

and this continues as qword, dqword.

So 101 could be read as "nibble-bit" and 1010 would be read as "byte-crumb." This all feels a little bit like Jabberwocky.

One source for this convention is this Wolfram page

Also see these Microsoft references: word dword qword

This answer has received some down votes based on the objection that this terminology is used typically when describing memory allocations. For example, a byte is any eight bit expression: 00000000 through 11111111. This is a fair objection. However, mathematicians often think of integers as the union of their predecessors, so $$8=\{7,6,5,4,3,2,1,0\}$$

Also I have see undergraduate computer science majors work as mentors in CS Scratch Clubs to help elementary and middle school children learn. I have seen them use base-two blocks and refer to them as bits, crumbs, nibbles, bytes. Kids giggled when they made up things like taking nibble out of bite and being left with two crumbs, etc. They had fun with the language and were learning place value. So in spite of the technical objection described above, the approach does have efficacy in teaching mathematics.

enter image description here

$\endgroup$
7
  • 2
    $\begingroup$ You called this a convention. Can you cite anywhere that it is used? $\endgroup$
    – Sue VanHattum
    Jun 23, 2023 at 16:32
  • $\begingroup$ Now I'm wondering what the time travel code in Bender's Big Score would be with this convention. $\endgroup$
    – Thierry
    Jun 23, 2023 at 16:42
  • 6
    $\begingroup$ These names don't correspond to binary numbers, but to the width of the binary number as represented in memory. For example, a byte is any eight bit expression: 00000000 through 11111111. $\endgroup$
    – Adam
    Jun 23, 2023 at 17:10
  • 1
    $\begingroup$ I saw a list like this long ago. I remember it included playte and tayble for the larger ones. $\endgroup$ Jun 23, 2023 at 20:11
  • 1
    $\begingroup$ @GeraldEdgar, I'VE FOUND THIS: en.wikipedia.org/wiki/Units_of_information $\endgroup$ Jun 25, 2023 at 13:33

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.