Basics of the seximal numbering system
The seximal (base-6) numbering system
is a positional numeral system (like the ubiquitous decimal system)
which uses six digits -- 0, 1, 2, 3, 4, and 5 --
instead of decimal's ten.
This is enough to write any number in seximal,
but it doesn't actually tell us how to refer to numbers in speech.
Fortunately for us, jan Misali,
in this video
and at seximal.net,
lays out just a system.
We'll cover the basics of that system here
with only minor differences.
Digit names
Each position in a number contains exacly one digit. In seximal, we use a subset of decimal's digits. This is also enough to count up to five (5):
- 0 - "zero"
- 1 - "one"
- 2 - "two"
- 3 - "three"
- 4 - "four"
- 5 - "five"
Counting in seximal
After "five" (5), we can continue to count the next six numbers using standard names, although the numerals are written differently than in decimal:
- 10 - "six"
- 11 - "seven"
- 12 - "eight"
- 13 - "nine"
- 14 - "ten"
- 15 - "eleven"
Sixes digit
After eleven (15) we have "twosy" (20), the first multiple of six, which can also be refered to by its other names "dozen" or "twelve". Numbers above this follow a pattern of "(sixes digit)-sy (ones digit)":
- 20 - "twosy" or "dozen"
- 21 - "twosy one"
- 22 - "twosy two"
- 23 - "twosy three"
- 24 - "twosy four"
- 25 - "twosy five"
- 30 - "thirsy"
- 31 - "thirsy one"
- 32 - "thirsy two"
- 33 - "thirsy three"
- 34 - "thirsy four"
- 35 - "thirsy five"
- 40 - "foursy"
- 41 - "foursy one"
- ...
- 45 - "foursy five"
- 50 - "fivesy"
- 51 - "fivesy one"
- ...
- 55 - "fivesy five"
"Nif"
The third position in seximal, 100 (36 in decimal), is called "nif". This term is borrowed from the Ndom language. Concatenating the value of the nif digit with the sixes+ones digits gets us up to "five nif fivesy five" (555):
- 100 - "nif"
- 101 - "nif one"
- ...
- 155 - "nif fivesy five"
- 200 - "two nif"
- 201 - "two nif one"
- ...
- 255 - "two nif fivesy five"
- 300 - "three nif"
- 301 - "three nif one"
- ...
- 355 - "three nif fivesy five"
- 400 - "four nif"
- 401 - "four nif one"
- ...
- 455 - "four nif fivesy five"
- 500 - "five nif"
- 501 - "five nif one"
- ...
- 555 - "five nif fivesy five"
But we can easily extend this by pairing digits so that the third and fourth positions count nifs:
- 1000 - "six nif"
- 1001 - "six nif one"
- ...
- 1555 - "eleven nif fivesy five"
- 2000 - "twosy nif"
- 2001 - "twosy nif one"
- ...
- 2555 - "twosy five nif fivesy five"
- 3000 - "thirsy nif"
- 3001 - "thirsy nif one"
- ...
- 3555 - "thirsy five nif fivesy five"
- 4000 - "foursy nif"
- 4001 - "foursy nif one"
- ...
- 4555 - "foursy five nif fivesy five"
- 5000 - "fivesy nif"
- 5001 - "fivesy nif one"
- ...
- 5555 - "fivesy five nif fivesy five"
Fractional numbers
Single-digit fractions in seximal are quite simple:
- 0.1 - "one sixth"
- 0.2 - "one third"
- 0.3 - "one half"
- 0.4 - "two thirds"
- 0.5 - "five sixths"
Alternatively, and for fractionals with more digits,
you can simply read the digits after the seximal point,
just like we do for decimal:
1.2345 - "one point two three four five".