3 ms·
Base-12 is nice because, like Seximal it is divisible by both the first and second prime number (2 and 3). But it is also divisible by the first prime (2) twice
by cjensen 8y ago
Base-12 is nice because, like Seximal it is divisible by both the first and second prime number (2 and 3). But it is also divisible by the first prime (2) twice, and doesn't immediately overflow into extra digits.
So 10 in base 12 can be exactly divided by 2, 3, 4, 6, 8, and 9.
Compare this to base 10 where 10 can only be exactly divided by 2, 4, 5, and 8.
- airstrike 8y agoHow exactly can 10 be divided by 4 and 8?
- deleted 8y ago[deleted]
- ythn 8y agoMaybe he meant you don't end up with a number with infinite digits? 10/4 = 2.5 vs. 10/3 = 3.33333...
- thomastjeffery 8y agoIn decimal: 10 / 4 = 2.5 2.5 can be represented exactly in decimal. As opposed to: 10 / 3 = 3.33333333333... which cannot. In duodecimal (10=dozen, A=ten): 10 / 3 = 4 A / 3 = 3.4
- gowld 8y agoyou need an extra blank line, or indent 3 spaces, to preserve linebreaks: 10 / 3 = 4 A / 3 = 3.4 10 / 3 = 4 A / 3 = 3.4
- thomastjeffery 8y agoUnfortunately, it is too late to edit; but thanks!
- dnautics 8y agoExact divisors are not what they are cracked up to be. By and large most divisions will wind up falling on an inexact division. One neat property of a prime base is that detecting exact divisions is easy: Just count trailing zeros in your result. E.g:. Ob110010 / 0b101 == 0b1010 which has the expected number of zeros at the end. You can't count on this in decimals, e.g. 50 / 25 == 2.
- jacobolus 8y ago> Exact divisors are not what they are cracked up to be. They’re pretty nice if you use base 60, in which case you can figure out how to almost always approximate any division problem by something you already have in your reciprocal table.
- thomastjeffery 8y agoBeing able to exactly divide by 3 is really helpful. That is why we use 12 for hours, inches, etc. I would consider a duodecimal (base-12) metric system to be ideal, personally.
- dnautics 8y agoConsider: take a log of all divisions done by your computer; how often would those divisions be done by something that is 3 or an exact multiple of 3.