A super easy way to pronounce binary numbers and numbers in some other number bases.
In schools and universities around the world, students are often invited or required to do arithmetic in base two, and/or in base eight. The students are often explicitly asked to compare base two or base eight with base ten. But the result is often a false comparison, because only base ten comes with a set of names for the powers of the base.
The base ten numbers are pronounced in a way that is appropriate for arithmetic, and by that I mean that 4567 is pronounced ‘four thousand five hundred sixty-seven, and not ‘four five six seven’. But the base eight numbers are pronounced like phone numbers, due to the lack of a good pronunciation system for base eight. The same thing applies to binary.
So I have created a unified pronunciation system for all bases that are a power of two: bases 2, 4, 8, 16, 32, 64, … ad infinitum. As far as I can tell, it is a completely original idea to use a single set of names for all bases that are a power of two.
I happen to like bases that are powers of two, and I think they should be used more often, but I will not be arguing that in this article. All I am arguing here is that if you are going to study or teach arithmetic in another base, you should make it easy for yourself by doing it in a way that is analogous to how you would do it in base ten, and not in a way that hamstrings you and/or your student.
Imagine for a moment counting or doing arithmetic in base ten while pronouncing the numbers like phone numbers. ‘One seven nine, one eight zero, one eight one, one eight two’ rather than ‘one hundred seventy nine, one hundred eighty, one hundred eighty-one, one hundred eighty-two’. ‘Two six plus two six equals five two’ instead of ‘ twenty-six plus twenty-six equals fifty-two’.
We don’t do it in base ten, not when counting or doing arithmetic, and with good reason. For the same reason, we shouldn’t do it when counting or doing arithmetic in other bases. But we do.
The lesson backfires. The aim is presumably to show how it’s perfectly possible to count and do arithmetic in base eight. But students come away with the impression that although it is technically possible, it’s unnatural and a bit of a nightmare. No one notices that it was bound to be like that when the numbers were pronounced like phone numbers.
The reason phone numbers are pronounced the way the are is to same time by stripping away the conventions for pronouncing numbers used for counting and calculation. In a classroom, there is no reason to do this, not even with binary, where the savings of time seem to be enormous and therefore the temptation is overwhelming.
It is of the nature of binary to be time-consuming to write and pronounce. Teachers should accept that.
Teachers would at present count to ten in binary like this: ‘one, one oh, one one, one oh oh, one oh one, one one oh, one one one, one oh oh oh, one oh oh one, one oh one oh’.
I would do it like this: one, two, two one, four, four one, four two, four two one, eight, eight one, eight two.
As you can see, my pronunciation system is in fact more concise, although that isn’t its primary purpose.
What about when the binary numbers are big? New short names are surely needed to replace the big powers two. I mean, ‘eight one, eight two’ is one thing, but ‘one thousand twenty-four one, one thousand twenty-four two’ is quite another.
Well, yes. My new name for one thousand twenty-four is ‘tis’. It’s pronounced ‘tiss’. Thus you count ’tis one, tis two’. I didn’t pull the name out of thin air. ‘Tis’ means two to the power ten (2¹⁰), which is one thousand twenty-four. The ‘t’ of ‘tis’ means ‘one’ and the ‘s’ means ‘zero’ and the ‘i’ means a positive power of two. Thus when you know the system you can deduce the number from it’s name.
Likewise, the name of two thousand forty-eight is ‘tit’, because it is two to the power eleven (2¹¹). ‘t’ means ‘one’, recall.
Four thousand ninety-six is ‘tin’, because ’n’ means ‘two’. And so on.
Here is the full set of rules for mapping the consonants to the ten numerals:
0 = s
1 = t
2 = n
3 = m
4 = r
5 = l
6 = sh
7 = k
8 = f
9 = p
Any power of two can be specified. Two to the power one hundred one (2¹⁰¹) is ‘tisit’, pronounced ‘tissit’. Two the power two hundred fifty-one (2²⁵¹) is ‘nilit’, pronounce ‘nillit’.
The great thing about a set of names for all power of two is that they are sufficient for all bases that are powers of two. Thus hexadecimal FFF + 1 = 1000 is pronounced ‘fifteen fi fifteen ri fifteen plus one equals tin’.
Or, if you prefer: ‘eff fi eff ri eff plus one equals tin’.
Or, if you prefer: ‘tel fi tel ri tel plus one equals tin.’ ‘Tel means fifteen because ‘e’ means a base ten number while ‘t’ and ‘l’ have their usual meanings (one and five).
Note: I am not endorsing the use of ‘F’ and to stand for fifteen. I use it because it is standard practice to do so when writing hexadecimal numbers, and the natural way to pronounce ‘F’ is ‘eff’.