A brief summary of my pronunciation for binary and other bases that are powers of two idea/tool.

We say a decimal number in one of two ways depending on the situation. If we are saying how old someone is, or how many jelly beans are on a plate, we say it as a normal number. If it is a zip code, telephone number, or password, we say it as digits. Usually we are in no doubt as to which way is right.

So we say “I’m thirty-one” and not I’m three one”. On the other hand, we say “My phone number is five five five five five five five” or “five double five double five double five”. We don’t say, “My phone number is five million five hundred fifty-five thousand five hundred fifty-five”. The wrong ways are unheard of, which is why it is quite comical to imagine someone saying them the wrong way.

The deeper lesson here may be that we take our dual pronunciation system for decimal for granted, and to a large extent apply its rules unconsciously (note that there is no word meaning pronounced as a normal number rather than as digits). This would come as no surprise to a linguist. After all, we apply the rules of English grammar mostly unconsciously — and they are much more complex than we think as well as different from what we think. Native speakers of English can rarely explain correctly how they know with absolute certainty something said in English is wrong or right grammatically. And when we say numbers, we are, after all, saying them in English.

Maybe this is why few to none noticed that other bases lack a similar dual pronunciation system. Ages in hexadecimal and all other bases are seemingly pronounced as digits and not as normal numbers.

Note: occasionally someone has devised a system for pronouncing numbers not only digit by digit but also, optionally, as normal numbers in another base but usually that system has never been used. I know only of one exception, and that is the case of base twelve and the way the dozenalists pronounce it, and specifically one man who uses base twelve instead of base ten whenever he can: Donald P Goodman, the president of the Dozenal Society of America. But seemingly he isn’t teaching base twelve to his children, and as far as I know he uses it alone, and not for communication with others. Source: this 2012 article:

Note that I am not advocating the abolition of decimal. I am not even saying we should use decimal any less (unlike Mr. Goodman). I’m saying that, ever since the publication of my idea, when we use another base that is a power of two and say a number in it we have a choice between saying it as digits and saying it as a normal number. What each person chooses in each situation should be up to the individual, just as it is with decimal. Presumably in other bases ages will be pronounced as normal numbers and codes as digits, the same as it is in decimal.

I think we should look into the idea of ‘multinumeracy’ to coin a term, by which I mean fluency in two or more number bases. Just as becoming fluent in French and/or Chinese doesn’t make us any less good at English, or use English any less (on the whole), becoming fluent in spoken hexadecimal and/or spoken binary won’t (I presume) make us any less good at decimal or use it any less (on the whole).

Scientists are saying early fluency in an additional language is good for the brain. Might it be the same for early fluency in an additional spoken base? In language speaking and listening form the foundation. Reading and writing piggyback on that foundation, to mix my metaphors awfully. We learn to speak base ten before we learn to write it, and that seems to work well. Shouldn’t we learn to speak and listen in binary (exercising our choice — perhaps unconsiously — between saying numbers as digits or normal numbers) before we learn to read and write it?

Some will fear that people will get confused by using two bases, especially at a young age. That is certainly a danger to be aware of. Maybe binumeracy or multinumeracy should be tried out by adults first to see what happens. If confusion is a problem, one way to prevent it might be to use new names for everything, perhaps even the names of the mathematical operations, ‘plus’, ‘minus’ and so on.

Thus spoken binary and its arithmetic would be like a foreign language. The number of beans on the table being specified might be the same, but that shouldn’t be a problem any more than the fact that the animal is the same whether referred to as ‘a cat’ or ‘un chat’.

I don’t want to digress much, so I’ll keep this short, but might it not be a way to overcome math phobia and other problems with learning arithmetic in other bases to teach arithmetic in another base or two as foreign language in effect? And being multinumerate at an early age could get people interested in and confident about math at an early age.

A simple way teach it would be for the student to listen to the spoken form and take it down as a dictation. Hearing ‘mi ni ti si’, the student would write ‘1111’. Hearing ‘ri mi’ the student would write ‘11000’. A series of numbers could be dictated slowly at first, and later at an increasing speed. The student would be in control of the speed, I would imagine.

Another way would be total immersion. No base ten numbers would be used for a few days, while games are played where numbers are constantly being spoken in the target base. Thus rather than studying the target spoken base, the student acquires the target spoken base. People who are good at French but bad at math might suddenly get a taste of what it is like to be good at math.

Maybe a foreign base could be taught as a separate subject, and not as part of math. It might make sense to teach it in the language lab. It might be a way to motivate a nerdy student to sign up for a language course.

Games played with numbers in base ten could be converted to the target base, e.g. monopoly could be played with octagonal dice and every number in base eight. Or a pure number game where player A always beats player B in base ten could be played in base sixteen which player B is good at, in effect a handicap for player A.

My system is the first, as far as I know, to have one set of names for all bases that are a power of two, with the names always having the same meaning across all those bases.

One should note that how the number is written often indicates whether it is a normal number or a telephone number or zip code number. “ The telephone number is 5,555,555.” puts the reader in a quandary. Does it mean there are that many telephones? Or that the telephone has some sort of IP address type thing?

The way a number is written can thus be used to cue people, e.g. employees in a company, how to pronounce a binary number, or a hexadecimal number. If a binary number lacks commas, it is a code number or data, and should be pronounced as digits, but if it has commas, it is a normal number, a number of jelly beans, say, and is to be pronounced as a normal number. Thus the incursion of my system into areas where it is not wanted can be prevented.

The idea is to use an easily learned (five minutes of memorization) algorithm to generate names for all the powers of two. These names are then used when counting using the ‘normal’ (meaning my new way that is the analogue of the normal way of pronouncing base ten numbers, i.e. using the names of the powers of the radix ) way of pronouncing binary numbers except when the as digits way is preferable.

Here’s all you need to memorize to be able deduce all my names for all powers of two. It’s the first ten names, from which all other names can be deduced: 2⁰ is ‘si’ (sounds like ‘sit’ with the ‘t’ dropped — the ‘i’ sound is always short like the ‘i’ of sit), then there is:……………………………………………………

2¹=ti, 2²=ni, 2³=mi, 2⁴=ri, 2⁵=li, 2⁶=shi, 2⁷=ki, 2⁸=fi, 2⁹=pi.

No need to say ‘one pi’ in binary, since it’s always one or none. So 2⁹ is ‘pi’ and not ‘one pi’. Would that even take you five minutes to memorize?

Now you can deduce the name of any power of two and vice versa. For example tin can be deduced to be 2¹² because ‘t’ means ‘1’ and ‘i’ means ‘two the power’ and ’n’ means ‘2’ which gives you ‘two to the power one two’ .

2¹⁰ can be deduced to be tis because ‘one zero’ becomes ‘t’ then ‘s’ with an ‘i’ in between. Simple, right?

It’s also extremely concise: 2⁹⁹ is pip. 2⁸⁸⁸ is fifif (pronounced ‘fiffif’). That’s a short name for such a big number: 2.06365051225e+267, i.e about ten to the power two hundred sixty-seven.

Note that with numbers smaller than sixteen you don’t really need new names, let alone numbers smaller than eight. Thus one might count one, two, two one, four, four one, four two, four two one, mi, mi one, mi two, mi two one… and not the ‘pure’ (base-ten-free) way of si, ti, ti si, ni, ni si, ni ti, ni ti si, mi, mi si, mi ti, mi ti si,… (Binary 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011,…)

An example or two will make this clear.

Note: the commas don’t need to be before each triplet of digits. They could be before each quadruplet or any other sized group of digits. I chose triplets because most people are familiar with them from base ten.

First consider binary 1,000,000,000,000. As digits: ‘one zero zero zero zero zero zero zero zero zero zero zero zero’. As a normal number (my new way for binary): ‘tin’.

Now consider binary 1,000,001,010,000. As digits: ‘one zero zero zero zero zero one zero one zero zero zero zero’. As a normal number: ‘tin shi ri’.

Now consider binary 1,111,111,111,111. As digits: ‘one one one one one one one one one one one one one’. As a normal number: ‘tin tit tis pi fi ki shi li ri mi ni ti si’. Note that only when the number is all ones is the normal way equally long (equal number of syllables though fewer letters). This one is the least favorable comparison for the ‘normal’ way (my new way for pronouncing binary that is analogous to the normal way of pronouncing base ten).

The binary names can be reused with every base that is a power two: base four, base eight, base sixteen, base thirty-two,… and so on.

Now consider octal10,000. Zip code way: ‘one zero zero zero zero’. ‘Normal’ way: ‘one tin’. Same name as binary 1,000,000,000,000, because it’s the same number of jelly beans except that it is ‘one tin’ rather than ‘tin’. 2¹² jelly beans. 8⁴ jelly beans. It’s the same. 2¹² = 8⁴. Even not knowing the base, there is no ambiguity about how many jelly beans are referred to.

Remember binary 1,000,001,010,000 that was ‘normally’ pronounced ‘tin shi ri’? Converted to base eight that would be octal 10,120. See how octal is binary in another form? As digits: ‘one zero one two zero’. As a normal number:: ‘tin shi two mi’. The only difference is that ‘ri’ has been replaced with ‘two mi’.

Octal 77,777 is next. As digits: ‘seven seven seven seven seven’. As a normal number: ‘seven tin seven pi seven shi seven mi seven’.

The system can cope with bases bigger than ten. Consider hexadecimal FFFF. As digits: ‘eff eff eff eff’. As a normal number: ‘eff tin eff fi eff ri eff’.

What about bases so big that one runs out of letters of the alphabet to use as numerals? No problem. We don’t actually need to use new symbols for numerals. For example hexadecimal FFFF could be written instead as hexadecimal [15][15][15][15]. ‘[15]’ is a new symbol/digit. As digits: ‘fifteen fifteen fifteen fifteen’. As a normal number: ‘‘fifteen tin fifteen fi fifteen ri fifteen’.

The numerals run from [00] to [15] so that each digit take up the same space.

Note that F and [15] could each be pronounced as ‘eff’ or ‘fifteen’ or even ‘eight four two one’ or ‘mi four two one’ or ‘mi ni ti si’).

Thus hexadecimal FFFF might be pronounced………………………………… ‘mi ni ti si tin mi ni ti si fi mi ni ti si ri mi ni ti si’.

Thus the fact that hexadecimal is a shorthand form of binary is made obvious. Hexadecimal FFFF is binary 1111,1111,1111,1111. I used quadrupletwise commas deliberately. The binary number as a normal number is:……………. til tir tim tin tit tis pi fi ki shi li ri mi ni ti si. No commas. Adding some commas for clarity gives us: …………………………………………………………….…til tir tim tin, tit tis pi fi, ki shi li ri, mi ni ti si. Interesting isn’t it?

My favorite activity is learning new things.

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