10 base ten is pretty arbitrary. Who's to say that's the most efficient? Why not 12? Why not 7? I'm not convinced. Anybody know what is or how to find out? I'll take anything. Please, throw out speculations. Remember: ancient civilizations like the Aztecs and Sumerians used base SIXTY! (60, 60, 24 ¦ ) It might end up being as big a number as that!
2007-08-07 05:28:24 · 4 answers · asked by Bennett 3 in Science & Mathematics ➔ Mathematics
"Efficient" is arbitrary, it's a trade-off.
If you used base-60, for example, you'd use less digits for numbers and calculations. BUT you'd have to know times-tables that are 36 times as large for 60*60 different digits instead of 10*10. So there'd be a lot more you'd have to learn before you could do calculations.
I suspect that 10 may not be the absolute optimum, but it's in a good position for a trade-off between number of digits and complexity of single-digit calculations -- and it's also divisible by 2 and 5 (unlike, say, 11 which is prime, or 9 which is only divisible by 3). I could see arguing for 8 (a power of 2) or 12 (lots of small factors) over 10, but they're all pretty much equivalent.
Computers use binary not because it is efficient for calculating, but because on/off for a tube (and later transistor) is the easiest and most obvious way to store information. When you think of it, binary is pretty inefficient in terms of the number of bits you have to sling around (which is why people use hex even though the computer doesn't).
2007-08-07 05:45:55 · answer #1 · answered by McFate 7 · 1⤊ 0⤋
Depends on what you are calculating. If you are adding to binary numbers then base 2 is the best base to calculate in. If you are performing calculations on base 10 numbers then base 10 is the best to work in. The real question would be "For a given application, what is the best base to measure information in?" and then use that base for the calculations as well. I exclude the purely theoretical mathematics because base should not mater in theoretical mathematics to begin with.
2007-08-07 12:34:00 · answer #2 · answered by Anonymous · 1⤊ 0⤋
If your doing the calculation by hand, then the larger the base, the easier it should be because the total number of digits your would be writing would be less. Make sense? i.e. writing 16 in decial take two characters 1 and 6. But writing 16 in hex only takes only characher -F
2007-08-07 12:33:59 · answer #3 · answered by Pawn 2 · 0⤊ 0⤋
Optimal in terms of efficiency is base two, this is why computers use it.
2007-08-07 12:37:24 · answer #4 · answered by btceng64 2 · 0⤊ 1⤋