# Big-endian is better than little-endian

This is a response to the post [We Write Numbers Backward](https://www.lsusr.com/blog/we-write-numbers-backward.html), in which lsusr argues that little-endian numerical notation is better than big-endian.[^5rgaakohy3p] I believe this is wrong, and big-endian has a significant advantage not considered by lsusr.

Lsusr describes reading the number "123" in little-endian, using the following algorithm:

*   Read the first digit, multiply it by its order of magnitude (one), and add it to the total. (Running total: ??? one.)
*   Read the second digit, multiply it by its order of magnitude (ten), and add it to the total. (Running total: ??? twenty one.)
*   Read the third digit, multiply it by its order of magnitude (one hundred), and add it to the total. (Arriving at three hundred and twenty one.)

He compares it with two algorithms for reading a big-endian number. One is using the same process as for a little-endian number, but from right to left. I agree with him that this is worse than the little-endian algorithm, because it is easier to read a number in the same direction as the text that surrounds it, which in English is from left to right.

The other big-endian algorithm is the one I observe myself as usually using. For "321", it is:

*   Count the digits (three), and convert that into an order of magnitude (one hundred). (Running total: ??? hundred ???.)
*   Read the first digit, multiply it by its order of magnitude (one hundred), and add it to the total. (Running total: three hundred ???.)
*   Read the second digit, multiply it by its order of magnitude (ten), and add it to the total. (Running total: three hundred and twenty ???.
*   Read the third digit, multiply it by its order of magnitude (one), and add it to the total. (Arriving at three hundred and twenty one.)

The point raised by lsusr against the big-endian algorithm is that we must count a number's digits before we can start reading them. He doesn't say explicitly why he dislikes this, but I can see three reasons:

1.  It makes the algorithm more complex.
2.  It makes the algorithm slower.
3.  It means we cannot begin the algorithm if we only have access to the beginning of a number.

Making the algorithm more complex is bad, but not very bad, because it is still fairly simple. It being slow to count all the digits in a number is a real problem, but we can usually solve it by separating groups of digits using commas or by using exponential notation. Finally, only having access the beginning of a number is not a very common situation in day-to-day life.

So these problems might not be that important, but they are still problems, so, if they were the only consideration, little-endian would be better. Then, what other advantage does big-endian have over little-endian?

Though it is not common for us to not be able to process the entire representation of a number, we often have reason not to need to. Numbers represent quantities, and sometimes we only want to know an approximation, not an exact quantity.

For example, if I look up the population of India, Wikipedia will tell me it was estimated to be 1,428,627,663 people (in big-endian notation), but I will usually have no reason not to think of it as "about 1.4 billion". By running the big-endian algorithm only partially, this is exactly what we get: an estimate of a number to some order of magnitude.

By contrast, after running the little-endian algorithm partially, we find the number's value modulo a power of ten. In most situations, that is completely useless. Besides, since the data on the population of India is actually an estimate from 2023, in that example, we also can be pretty sure the least significant digits aren't even accurate.

What if you are not a person, but a computer, converting a string into an integer? In that case, having a simpler and faster algorithm is important, having to start with only the beginning of a string (what the user has typed so far) is plausible, and knowing the number's approximate value is useless. So in this case the little-endian algorithm is much better than the big-endian one.

But there is another algorithm that can be used by a computer for parsing big-endian numbers. Operating on "321":

*   Read the first digit and add it to the total. (Running total: three.)
*   Read the second digit. Multiply the total by ten, and add the digit to the total. (Running total: thirty two.)
*   Read the third digit. Multiply the total by ten, and add the digit to the total. (Arriving at three hundred and twenty one.)

This algorithm operates sequentially on the string, and it is even simpler and faster than the little-endian algorithm, because it doesn't have to keep track of the order of magnitude. So for computers, too, reading big-endian is easier.[^gtas1kdic6]

So why do humans use the previous algorithm to read numbers, instead of this one? For the same reason we prefer big-endian to little-endian: successive approximations that narrow down on a number are more useful than operations for which the state in the middle is useless.

Lsusr's article ends by claiming the inventor of Arabic numerals knew little-endian numbers were better, and used them, because Arabic is written right-to-left. But positional decimal notation was not invented by the Arabs. It was invented by the Hindus, and brought to Europe by the Arabs. And the Hindus used the [Brahmi script](https://en.wikipedia.org/wiki/Brahmi_script), which is written left-to-right. Therefore, the inventor of the Hindu-Arabic numeric system used big-endian notation.

[^5rgaakohy3p]: Lsusr's post has a good explanation of what little-endian and big-endian mean, so I won't repeat it here. 

[^gtas1kdic6]: Of course, there could be an even simpler little-endian algorithm I can't think of. If you know one, let me know.