;Why does storage come in the form of a number Which is always the exponential form of 2 ?

72 views
0

Such as 8gbs, 16, 32 ,64 etc.

In: Technology

For physical hardware reasons.

If you imagine a very simple computer with 1 bit of storage, you need 1 physical *connection* to access it and it can be one of two things – a 0 or a 1, binary.

2 connections to 2 bits of storage gives *four* possible settings – 00, or 01, or 10, or 11.

3 connections to 3 bits of storage gives *eight* possible settings.

4 gives 16

5 gives 32

6 gives 64

(..)

32 connections to 32 bits gives 4,294,967,296 possible settings. Or 4 gigabytes.

Hard drive storage doesn’t necessarily always come in this form. For instance, I have a storage server full of 10TB hard drives, not 8 or 16s.

However, what does happen is that a hard drive controller may be a limiting factor. These are what actually allow us to map every part of the hard drive. Since every spot on the hard drive needs an address, this is where we run into problems.

Let’s say, for argument’s sake, that we want to be able to start reading or writing from any byte on the hard drive. This means we need to address all of them. On a 256GB hard drive, this is 274877906944 different addresses. (256GB/MB * 1024MB/KB *1024KB/B * 1024B). I make my hard drive controller able to address this many specific bytes. I can use this controller for any hard drive up to 256GB in size, but not more. If I want a 300GB hard drive, I would need a controller that can do up to a 512GB hard drive. This is why you might see some drives that go up to that level to specifically.

(In practice, you actually address blocks that are a set size wide, but the logic remains true even when you do that).

Everything a computer does, it does in binary – everything is represented with 1 or 0. So, how many unique pieces of data you can store is always a function of how many 1s and 0s you can store and address. This means that your storage capability is always going to be a factor of 2, and with a few exceptions even more precisely, 2 to an exponent less 1.

1 3 7 15 31 63 127 255 511 1023 2047 etc.

What those numbers have in common is that in binary, they are all 1s. 1. 11 111 1111 11111 etc.

It is the equivalent of Saying in decimal that a cash register or counter will always have a limit that is 10 to an exponent – 1, meaning a number that Is all 9s. Your counter can count to 9, or 99, or 999 etc. A counter that could only count to 998 would be silly.

Similarly, a binary counter can always count to 1 11, 111, 1111, 11111 etc.