We use base 10 with 0-9 digits and each position is a ten’s place, and the efficiency being measured is the product of the number of digits and the length of digits needed to represent a number in a given range of values. So if we used base 2 binary instead of base 10 decimal we only need to remember 2 digits 0-1, but to represent most numbers we’ll need more digits, 11 in base 10 is 1011 in base 2. On the other side we could use hexadecimal to write shorter numbers like 11 is B, but need to use more digits, 0-F digits where A-F are the 10-15 digits.
If you try to plot a function that minimizes the efficiency the minimum is at e. So you’d have digits 0-2 and e would be written as 10 since each position is an e’s place.
The most efficient base for a number system is e.
We use base 10 with 0-9 digits and each position is a ten’s place, and the efficiency being measured is the product of the number of digits and the length of digits needed to represent a number in a given range of values. So if we used base 2 binary instead of base 10 decimal we only need to remember 2 digits 0-1, but to represent most numbers we’ll need more digits, 11 in base 10 is 1011 in base 2. On the other side we could use hexadecimal to write shorter numbers like 11 is B, but need to use more digits, 0-F digits where A-F are the 10-15 digits.
If you try to plot a function that minimizes the efficiency the minimum is at e. So you’d have digits 0-2 and e would be written as 10 since each position is an e’s place.
This is not a great explanation of radix economy of Base e.