How octal numbers should be pronounced by math teachers.

Note: You should consider reading https://bartshmatthew.medium.com/how-a-math-teacher-should-pronounce-a-binary-number-1c41773df52f before reading this, as this article follows on from it.

The situation with pronunciation of octal is the much the same as with pronunciation of binary numbers, as I described in the article linked to above.

To use the same example as I did with binary, which is fourteen: in math class 16eight is typically pronounced ‘one six’ or ‘one five base eight’. This works but is far from ideal, because in math class a number is not data like a telephone number or a code number used in machine code, but rather a quantity. Reciting the numerals is what we do in decimal with phone numbers, not with quantities. We don’t say that the population of the United States is ‘three five zero zero zero zero zero zero zero’. We say it is ‘three hundred fifty million’, and with good reason. Those reasons apply equally well to pronunciation of octal.

Some people would pronounce it ‘sixteen base eight’, which could be misunderstood to mean 20eight and it’s very difficult to avoid this ambiguity. And anyway, it’s a nonsense. Sixteen is six plus ten. It is fifteen plus one.

Some would say you should pronounce 16eight as ‘fourteen octal’. In the first place, this is not really pronouncing 16eight, rather it is translating it into 14ten and pronouncing that, and even then arguably wrongly. Shouldn’t it be ‘fourteen decimal’ ? In the second place, you are liable to be understood as meaning 14eight. See my article on pronouncing binary, linked to at the top, for more.

As with binary, a system of pronunciation of binary for use when doing binary arithmetic that is analogous to how we pronounce base ten when doing arithmetic is sorely lacking.

My pronunciation system is optimized for simplicity of understanding and ease of learning by the teacher and subsequently, students of all ages. It is designed to be as simple and regular as possible. It is thus ideal as a starting point for modifications and experiments.

It is not optimized for having no traces of base ten in it, nor for being as close an analogy to base ten as possible. For example, there is nothing in it that corresponds to ‘twelve’ which is remarkable for being a single syllable. There is nothing analogous to the ‘teen’ numbers of base ten.

My system could be modified to make it a closer analogy of base ten.

French speakers could modify my system to make it more analogous to how base ten is pronounced in French. In French, 100ten is pronounced ‘cent’ and so a French version of my system might have 100eight pronounced not as ‘one shi’ but as ‘shi’. British English speakers might prefer to pronounce 101eight as ‘a shi and one’ instead of ‘one shi one’ because they pronounce 101ten as ‘a hundred and one’.

‘Myriad is a noun and an adjective. As a noun, it means either 10,000 precisely or a great number generally.’, says writersdigest.com.

In base ten we say ‘ten thousand’ and not ‘two myriad’. My system could be modified to make it so you likewise pronounce 10,000eight as one mi pi instead of my present one tin. The latter is the analogue of one myriad.

My system for counting out loud writing longhand in octal is:

1eight, pronounced ‘one’.

2eight, pronounced ‘two’.

3eight, pronounced ‘three’.

4eight, pronounced ‘four’.

5eight, pronounced ‘five’.

6eight, pronounced ‘six’.

7eight, pronounced ‘seven’.

10eight, pronounced ‘one mi’. Or ‘one eight’ (mi is 2³, which is eight). To keep it simple I will use ‘mi’ rather than ‘eight’, everywhere in this article but that doesn’t imply it’s better than eight, only that it is perhaps less confusing.

Note: ‘one mi’ means ‘a mi’, just as ‘one hundred’ means ‘a hundred’ (in base ten).

11eight, pronounced ‘one mi one’. Or ‘one eight one’.

Note: Analogous in pronunciation to ‘one hundred one’ or ‘one thousand one’.

12eight, pronounced ‘one mi two’.

13eight, pronounced ‘one mi three’.

14eight, pronounced ‘one mi four’.

15eight, pronounced ‘one mi five’.

16eight, pronounced ‘one mi six’.

17eight, pronounced ‘one mi’ seven.

20eight, pronounced ‘two mi’. Or ‘two eight’.

Note that ‘two mi’ is analogous in pronunciation to ‘two hundred’ and just as there is no need for an ‘s’ on the end of the word ‘hundred’, there is no need for an ‘s’ on the end of ‘mi’, even though there are two hundreds, two “mi’s”.

21eight, ‘two mi one’ .

Note: ‘two mi one’ is pronounced analogously to base ten’s ‘two hundred one’. Likewise, ‘two eight one’ which is also okay.

22eight, pronounced ‘two mi two’.

23eight, pronounced ‘two mi three’

… (skipping ahead)

30eight, pronounced ‘three mi’.

76eight, pronounced ‘seven mi six’.

77eight, pronounced ‘seven mi seven’.

100eight, pronounced ‘one shi’. ‘One sixty-four’ is technically okay, but unwieldy, and therefore not recommended.

Note: Recall that ‘shi’ is the word meaning 2⁶ that I used in the article on binary as the name for 1,000,000two. The name is reused in base eight without the slightest possibility of confusion, because 2⁶ = 8² = 64. 64ten that is, commonly known as ‘sixty-four’. The word has the exact same meaning and pronunciation in every base, being written using a different string of numerals in different bases. When hearing ‘shi’ out of context, the only ambiguity is the base. The number itself is always 64ten. To summarize, 1,000,000two = shi = 100eight.

101eight, pronounced ‘one shi one’. ‘One sixty-four one’ is not recommended.

102eight, pronounced ‘one shi two’. ‘One sixty-four two’ is not recommended.

103eight, pronounced ‘one shi three’. ‘One sixty-four three’ is unwieldy.

104eight, pronounced ‘one shi four’. ‘One sixty-four four’ is very unwieldy.

177eight, pronounced ‘one shi seven mi seven’.

200eight, pronounced ‘two shi’.

777eight, pronounced ‘seven shi seven mi seven’.

1,000eight, pronounced ‘pi’.

Remember ‘pi’ from my article. Pronounced like ‘pit’ with the ‘t’ sound dropped, not like ‘pie’.

7,777eight, pronounced ‘seven pi seven shi seven mi seven’.

10,000eight, pronounced ‘tin’.

… and so on.

To see how the names are generated by an algorithm so that no name need to be memorized, only the algorithm, look at the article linked to at the top. Note that students don’t need to know the how the names are generated. If only a small base eight numbers are used as examples, it’s probably best to leave that until after they have learned (by rote or otherwise) ‘mi’, ‘shi’, ‘pi’, and ‘tin’ , say, and have mastered using them in octal counting and arithmetic.

Some examples of octal arithmetic pronounced my way.

1,000eight + 1,000eight = 2,000eight

‘one pi plus one pi equals two pi’.

3,000eight × 3,000eight = 9,000,000eight

‘three pi times three pi equals nine tif’.

1,111eight × 50eight = 55,550eight

‘one pi one shi one mi one times five mi equals five tin five pi five shi five mi five’