GiB explained

kekoa

MiB, GiB are using binary prefixes (powers of two) to show magnitude, while MB, GB are using decimal prefixes. These prefixes have nothing to do whether some physical memory (hard drive) is formatted or not.
Binary prefixes have been introduced to *avoid* confusion.
When you're dealing with small qantities, the difference doesn't show much; e.g. 1 KB = 1'000 Byte, whereas 1 KiB = 1'024 Byte. Almost nobody will complain about the 2.3% missing. But take larger quantities and the difference really shows:
A Giga is defined as 1'000'000'000 = 10^9; a Gibi as 2^30 = 1024 x 1024 x 1024 = 1'073'741'824 (same magnitude, but slightly more).
Therefore a 160 GB hard drive has a capacity of 160 x 10^9 Byte; any computer (knowing only binary) will report 160 x 10^9 / 2^30 = 149 GiB; a 250 GB drive will be (correctly) seen as 233 GiB (in most cases still labelled GB, that's the confusion).
The companies selling hard drives will gladly use the higher number (160; 250) as a sales argument.
For further reading, see this article: "http://en.wikipedia.org/wiki/Binary_prefix".

Addis

Kekoa is right, it's unrelated to the formatting of the disk.

Technically when Windows displays a file size, it should say KiB, MiB etc rather than KB, MB.

Can be quite confusing, especially since Mb isn't megabyte but megabit.

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donkey42

makes sense now if seen it, but i always thought Mb = megabyte, but, can i see the logic

BTW:TBH: i just ignored kekoa because it went wwwooossshhh over my head, i never was good at maths

Edit: sorry kekoa

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kekoa

donkey42: Tried to put it in a way as not to intimidate anybody, sorry if I missed...
I've always admired the boldness of *applied* math.
In my opinion, the approximate equation
10^3 = 1'000 = 10 x 10 x 10 (approx) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1'024 = 2^10
is a fine example of engineering math dating from the age of the slide rule and early computing machines.

donkey42

well my interpretation is 10^3 = 1 & 3 zeroswith youunderstand that bit nowi don't understandhow does 2^10 differ by being the reverse (nearly) of 10^3, how does that equate ?

Edit: me too, i just can't get my head around it

Edit: i just can't understand 1024 = 2^10 ?

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kekoa

donkey42: Will try to help you figuring this out...

This sign "^" should stay for "to the power of"; So "a^m" means "a to the power of m". ---

Hence "10^3" means "ten to the power of 3", which translates to "multiply 10 three times by itself" which equals 1'000 (10 x 10 x 10). In this construction 10 is called the "base" and 3 is called the "exponent". Yes, you're right, the exponent 3 means a 1 followed by three 0, as we're in the realm of our everyday *decimal* (base 10) system which knows ten digits (0 | 1 | .... | 8 | 9). Once you've reached 9 while counting, you'll have reached the base limit and have to use your carry digit so as next after 9 comes 10 (one, zero). ---

Then we have another power "2^10", which translates to "multiply 2 ten times by itself", 2 being the base and 10 being the exponent. Now we're dealing with the *binary* system (base 2) which knows only two digits (0 | 1). (These two digits are equivalent to two defined "states" in a computing machine.) Here comes a small comparison table:

decimal | binary

0 | 0000
1 | 0001
2 | 0010
3 | 0011
4 | 0100
5 | 0101
6 | 0110
7 | 0111

8 | 1000
...

The last (9th) row implies 2^3 = 8 which means that you are going to need 3 binary places to cater for decimal digits 0 through 7. Or put the other way around, groups of binaries (3 each) may be shortened to 1 octal (programmers use that property sometimes). Our decimal 8 translates to a 1 followed by three 0 in binary notation.

As you'll see, as there are only digits zero and one, the carry-over has to occur much earlier (in the row of decimal 2). Our decimal 2 is 10 (one, zero) in binary speak...
To follow your rationale, "2^10" (= 1'024, that's our decimal notation) should sport ten zeros; you're right, if you wrote it out in *binary* (think of continuing the above table) it would look indeed like this (as expected): 10'000'000'000 (b). That's how a computer would internally store our decimal number 1'024 by using up 11 bits of memory...

Addis

In short, 1KiB is 1024 bytes. 1KB is 1000 bytes. Therefore, 50 KiB is greater than 50KB.

Manufacturers use the decimal prefix because they can call a 260GiB drive a 300GB one, for marketing reasons.

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donkey42

i've had a quick look at it, but, i need my thinking head on to figure it out, kinda like worzel gummage, i'll look at it later, cheers kekoa & Addis

Edit: thank you both, it seem really simple now, thankies for spelling it out for me cheers

BTW: i want a slide rule, now i know what they exist for, thanks

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