How many kilobytes exist in nature?

Question

Mathematics

The question arose when trying to deal with new systems for storing content, in particular, IPFS.
How to correctly calculate how many binary variants of one kilobyte exist?
I calculated it like this: 8192x8192
And it turned out a little over 67 million.
Even somehow not a little. Mistake?

Answer 1

2 ⁸⁰⁰⁰ or 2 ⁸¹⁹² , depending on what you mean by kilobyte
Each bit position can be 0 or 1, two options for each of 8000 (8192) positions.

Answer 2

There are 1000 bytes in a kilobyte (depending on the memory microarchitecture, somewhere around 1024), or 8000 bits, which in turn can take the value 0 or 1. That is, we have 8 thousand places and each of which can take two different values (0 and 1). Let's count how many options for 2 bits: in the first place there can be two options (0 and 1), in the second there are also 2 options (0 and 1), we multiply them and get 4. Why did we multiply them? Multiplication shows how many times we must take a number: 2*5 - 2 must be taken 5 times: 2+2+2+2+2=10, so in our example we have to take 2 options from the first place twice, once for 0, the second time for 1: 00, 10 for zero, 01.11 for 1. So we got 4 options for 2 places, and we have 8 thousand of these places, therefore, we need to multiply 2 by 2 in the amount of 8 thousand, for this there is a degree (shows how many times we have to multiply the number by itself): 2 to the power of 8 thousand, it remains to count.