Continuing off my previous post

24 bits are kinda trash for storing numbers through the prime factor format. But 24 bits is even less than ordinary integers, and maybe we can do better. If we allow upto 32 bits (like ordinary ints), then we have 6 more bits for adding in 11 as a prime factor as well as 2 leftover bits. One of those bits could be a sign, allowing for negative numbers. Another could be fucking anything idk.

Now this way of doing things ... isn't not necessarily too bad, but we could try to improve?

First, we can store the exponents as a 2's complement. Search it up. It's slightly more efficient than storing signed integers. Basically in signed ints, +0 and -0 are stored as 2 seperate numbers even though they are functionally the same. In 2s complement, this is fixed.

I had 6 bit for the exponent. 1 for the sign. 3 for the powers (upto 7th power). 2 for the roots (upto 4rth root)

With 2's complement we can change to 4 bits for the powers and 2 for the roots. This allows the powers to range from -8 to +7

Which is ... wierd? And stupid? I don't think -8 is a very common power to use. Imagine being able to store 1/256 exactly, but not 13. A better way imo is to go 2 bits for the powers and 2 for the roots. This restricts the powers down to -4 to 3 which isn't super nice, but has the advantage that prime factors are now stored as 4 bit blocks. This plays nicely with the computer.

Now I introduce my next trick. Not every prime factor is equal. 2 and 5 are important. So I can give 8 bits to the each of them. That's 16 bits. Then the remaining 16 bits are divided into 4 other prime factors (3, 7, 11 and 13).