How a math teacher should pronounce a binary number.

Why current pronunciation systems for binary are inadequate for the math classroom.

Let’s dive in using fourteen as an example.

Counting aloud in binary using my pronunciation system.

Try counting from one to sixteen in binary, pronouncing the binary numbers in a way that is roughly analogous to how you’d do it in base ten:

The new names only variant.

If you want to get as far as possible from base ten, using my system, or to make it clear which base you are using without saying it, you should use only the new names, including the optional ones: ‘si’, ‘ti’, ‘ni’, and ‘mi’ instead of ‘one’, ‘two’, ‘four’, and ‘eight’, respectively.

How the infinite set of names were generated, and how they can be deduced from the numbers and vice versa.

It’s time to share the rules that allow the names of each binary number to be deduced. Note that the math teacher does not need to share these rules with the students, because the latter do not need to know them to count and do arithmetic in binary using the names.

Uses for my pronunciation system in the classroom.

A simple way to get students familiar with binary numbers is for the teacher to dictate (or play a recording of) some binary numbers while the students write them down. For example, the teacher says, ‘ eight four two one’ or ‘mi ni ti si’ and the student writes down, ‘1,111’ (or ‘1,111two’ if it needs to be distinct from decimal).

A final comparison with other methods of pronouncing binary numbers.

By the way, imagine what a mess it would be if the teacher dictated, using that method that is so often voted up on the Internet answer sites when binary is asked about, ‘eleven times eleven’, and the student wrote down the answer in longhand as, ‘one thousand one’. The student is liable to forget in which base eleven time eleven equals one hundred twenty-one. Bear in mind that the student may well also be studying base eight and/or base sixteen and/or base twelve and/or base six, and presumably pronouncing ‘11’ as eleven in all of them.

How concise is my system?

Very concise. 1,111,111,111two pronounced as a string of numerals would be ‘one one one one one one one one one one binary’. Thirteen syllables including ‘binary’). With my system, which needs no ‘binary’ to disambiguate the base in order to disambiguate the number, it is ‘pi fi ki shi li ri mi ni ti si’ which is ten syllables. Three syllables fewer. And this is the least flattering example. Replace any one of those one’s with a zero and you need to add a syllable (if it will be pronounced ‘zero’) to the telephone number style recitation of the numerals, while subtracting a syllable from my pronunciation of it.

Binary fractions.

In decimal we pronounce 12.19ten as ‘twelve point one nine’.

Unfortunate names generated by the algorithm.

2¹¹ is/would be ‘tit’, which is not too upsetting because it’s the name of a type of bird, but 2⁶¹ is/would be ‘sh*t’, and 2⁹⁰ is/would be ‘pis’. 2⁶¹ definitely needs a new name. Some possible substitutes would be: shith, shid, chit, chid, and chith. I think that ideally an algorithm would determine how unfortunate names would be changed. Which names are unfortunate enough to need changing is subjective and ever changing as slang words are coined or drop out of use, and so perhaps the best thing at this stage is just to let the algorithm do its thing, but make the system customizable by users, and let users decide which names are too unfortunate. For example, a teacher who is using the system in school will probably want ‘sh*t’ changed to something else, but maybe someone using it in a video on his or her own website wouldn’t care. Fortunately they are rare, about one percent to three percent of the powers of two.

Further reading.

What you have seen in this article is just the tip of an iceberg. To keep things simple, I have limited myself to discussing binary. But my infinite set of names for the powers of two is sufficient for any base that is based on a power of two. That means octal, hexadecimal, as well as base four, base thirty-two, base sixty-four, and so on. Infinitely many bases, each with an infinite number of powers of two, each one with a name taken from binary.

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Matthew Christopher Bartsh

Matthew Christopher Bartsh

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