A neglected aspect of teaching binary is the question of how to pronounce it. I will deal with this question.
In computer science it often makes sense to pronounce binary numbers like telephone numbers; a mere series of numerals. But in a math class, quantities are being considered, and a comparison with base ten counting and arithmetic is implicit if not explicit.
Current pronunciation systems for binary are inadequate. That is why binary numbers when being taught to beginners, for example fifth graders, should be pronounced in a way that is analogous to how the teacher has been pronouncing base ten numbers when doing counting and arithmetic, and not analogous to how the teacher recites a telephone number.
Let’s dive in using fourteen as an example.
Fourteen, when converted from our everyday base ten to a binary number is written ‘1110'. Sometimes a subscript ‘two’ or subscript ‘2’ is appended making it ‘1110two’ or ‘1110₂’. Note that this seems to be best that Medium.com can do to display a subscript ‘two’ or ‘2’. I will use ‘1110two’ as being the safer, less ambiguous format.
Most math teachers pronounce 1110two ‘one one one oh base two’, or ‘one one one zero base two’, or if the context makes it unambiguous, just ‘one one one oh’, or ‘one one one zero’. This works, but it is not ideal because one is simply reading out the digits. It is like pronouncing ‘27’ as ‘two seven’ rather than ‘twenty-seven’. Or pronouncing 7² as ‘seven superscript two’ rather than ‘seven squared’. Or pronouncing French ‘chat’ (which is pronounced in French roughly as ‘shah’ and means ‘cat’ — the meowing animal) as ‘see aitch ay tee’.
Not many math teachers, thank goodness, would pronounce 14 ÷ 2 as ‘one four divided by two’. But when teaching arithmetic in binary, the teacher probably would pronounce the exact same problem, 1110two ÷ 10two as ‘one one one zero divided by one zero’. This seems to be a great pity. The reason for it may be the lack of a well-known way to pronounce binary numbers that is analogous to the way we pronounce base ten numbers when doing arithmetic or counting.
I say ‘when doing arithmetic or counting’ because when the number is merely a phone number or other code or data, and therefore not a number that that represents a quantity, and not a number whose magnitude needs to be understood, and not a number that will be used in any calculation, then it is fine and very efficient to recite the string of numerals.
You could probably find a math teacher who ‘pronounces’ 1110two as ‘fourteen’. This also works, but it is not ideal because it is not so much pronouncing the binary number as calculating the decimal representation and pronouncing that. It is like ‘pronouncing’ 7² as ‘forty-nine’, or ‘pronouncing’ French ‘chat’ as ‘cat’, which would be calculating what 7² is and pronouncing that, and translating French ‘chat’ into English ‘cat’ and pronouncing that.
Perhaps half of all people that have an opinion on it, if the Internet ‘answers’ sites are to go by, think that 1110two should be pronounced ‘one thousand one hundred ten base two’. This is a terrible method, because that way you can never safely shorten it to just ‘one thousand one hundred ten’ because of the danger of it being understood as being the familiar one thousand one hundred ten (of base ten). Also, there will always be the danger that you will be understood to mean 10001010110two which is 1110ten converted to a binary format. There is no way to make the listener understand that you don’t mean the latter, no matter how you phrase it. Whether you say ‘one thousand one hundred in/written in/read as/base two’ it will never be clear that you don’t mean 10001010110two. It is like pronouncing French ‘chat’ as English ‘chat’ (as ‘chit-chat’).
If you demonstrate or teach counting, arithmetic, and measuring in binary while reciting the numbers like phone numbers, you will have a false comparison with decimal unless you pronounce the decimal numbers in the same way.
It is for the above reasons that I propose that math teachers, and indeed anyone who wishes to appreciate arithmetic, counting, measurement, and other mathematical thinking using binary numbers should pronounce binary numbers in a way that is analogous to how we pronounce our everyday base ten numbers when not reciting a phone number or a room number or other code or data.
If you demonstrate or teach counting, arithmetic, and measuring in binary while reciting the numbers like phone numbers, you will have a false comparison with decimal unless you pronounce the decimal numbers in the same way.
The student has little chance of appreciating the full beauty and power of binary when all numbers are reduced to strings of numerals pronounced like binary telephone numbers. And with decimal counting using normal good decimal pronunciation being compared with binary counting using mere recitation of numerals the student cannot make an accurate or enlightened comparison between the two bases.
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:
1two, pronounced ‘one’. Note that 1two is analogous to 1ten because each is the smallest number and the smallest numeral in its base, but also to 9ten because each is the biggest single digit number and the biggest numeral in its base.
10two, pronounced ‘two’. Note that 10two is analogous to 10ten because each is the smallest two digit number.
11two, pronounced ‘two one’. Note that 11two is analogous 11ten because it is one more than 10two but also to 19ten because each is the largest two digit number that starts with a ‘1’ and also to 99ten because each is the largest two digit number.
100two, pronounced ‘four’. Note that 100two is analogous to 100ten because each is the smallest three digit number but also analogous to 900ten because each is the biggest three digit number that ends in ‘00’.
101two, pronounced ‘four one’. Note that 101two is analogous to 101ten because each is one bigger than the smallest three digit number in its base. This is not the only analogy here.
110two, pronounced ‘four two’.
‘111two, pronounced ‘four two one’. Note that 111two is analogous to 999ten because each is the largest three digit number in its base.
1001two, pronounced ‘eight one’.
1010two, pronounced ‘eight two’.
1011two, pronounced ‘eight two one’.
1100two, pronounced ‘eight four’.
1101two, pronounced ‘eight four one’.
1110two, pronounced ‘eight four two’.
1111two, pronounced ‘eight four two one’.
10000two, pronounced…what? ‘Sixteen’ would seem to be the logically implied name. But ‘sixteen’ is a base ten number. It’s short for ‘six and ten’. That’s confusing. And it will be worse when we get to bigger numbers. ‘Thirty-two’ (‘three tens and two’), ‘sixty-four’ (‘six tens and four’), and ‘one hundred twenty eight’(ten tens and two tens and eight’, and so on, getting longer and longer and more and more difficult and confusing and more and more obviously being base ten numbers.
The solution is to find short, easily pronounced and easily recalled names to replace ‘sixteen’ for 10000two, ‘thirty-two’ for 100000two, and so on. But there are an awful lot of names needed, because binary numbers are so long. Compare 1000two with 8ten. It’s four digits compared with one. So these names should be super easy to recall, because so many are needed and no one will be able to face learning so many names unless they are super duper easy to learn.
The easiest to recall names would be names that can be deduced from the number. This way, no names need to be memorized, only the way to deduce the name from the number needs be memorized.
But for now, to keep things simple, I’ll just tell you that my new name for 10000two is ‘ri’ and my new name for 100000two is ‘li’, and my new name for 1000000two is ‘shi’. 10000000two is ‘ki’. 100000000two is ‘fi’. 1000000000two is ‘pi’.
