Please help me understand - 4.7g DVD is actually 4.37g. ???

[blinky88]

I have read about this many times and cannot make sense of the mathmatics behind the explanation. If a gigabyte in the real world is 1,000,000,000 bytes and is 1,024,000,000 in computer terms, the difference is 2.344% .... if a 4.7g DVD is actually 4.37g, the difference is 7%. If those perecentages are accurate the explanation of 1,000,000,000 being 1,024,000,000 cannot be the only factor. One would think 4700000000/1024 would give you the correct answer. Can someone please explain what other factors come into the calculation. I have seen a calculation on these forums explaning the correct formula which is: 4700000000/1024/1024/1024. Why is dividing the total by 1024 3 times by 1024 3 times doesn't seem to be logical.
Thanks to those who respond.

[Baldrick]

1KB is 1024 bytes
1MB is 1 048 576 bytes (1024bytes x 1024bytes)
1GB is 1 073 741 824 bytes (1024bytes x 1024bytes x 1024bytes)

[aggies11]

The difference isn't just between GB. It happens in each unit of measure, so that the effects become cummulatively larger and larger, the higher you get.

In *real* computer math, Each unit is 1024. Further, to get to the next unit, you need 1024 of the previous unit. So that not only is a Kilobyte 1024 bytes. But a Megabyte is 1024 kilobytes. And a GB is 1024Megabytes. etc.

In the "faulty" math, which uses standard "metric style" measurements (even though bytes and bits are not metric units!!), it's based on 1000. Each unit is 1000. And it takes 1000 of them to make the next unit.

So as you can see, the more units (larger) you go up from the basic byte, the bigger the difference is.

1000 x 1000 x 1000 x 1000 ....
vs
1024 x 1024 x 1024 x 1024 .....

Hopefully that helps

Aggies

[vuphan]

4.7GB is 4.7GB. It is a raw format. But usable or writeable is 4.37Gb. the waste space is for file system format. It is similar to your hard disk. 18GB is raw, usable is some where 16.7GB, the waste space is depending type of file system format (ntfs, fat, ufs, cdrom hsfs, etc...)

my 2 cents

[DBeeD]

In the real world, we can use base 10 Computers use base 2. The prefixes kilo=1000, mega=1,000,000, giga=1,000,000,000 and so on. With base 10, you can actually get 1000, just 10^3. However, with computers since you're using base 2, the closest thing you can get to 1000 is 2^10 which equals 1024, so they refer to this as kilobyte even though kilo really means 1000. With base 10 you can get mega by going 10^6, with base 2 the closes thing is 2^20 which equals 1048576, they call this a megabyte which should mean 1 million bytes. Billion or Giga is 2^30 instead of 10^9 and so on.

So with dvds, it has 4,700,000,000 bytes (4.7 billion(10^9) bytes). But 4,700,000,000/gigabyte(2^30)= 4.38GB

[Baldrick]

4.7GB is 4.7GB. It is a raw format. But usable or writeable is 4.37Gb. the waste space is for file system format. It is similar to your hard disk. 18GB is raw, usable is some where 16.7GB, the waste space is depending type of file system format (ntfs, fat, ufs, cdrom hsfs, etc...)

my 2 cents

no.

[porphyra]

I second that No. No No.

[aggies11]

Aiyeee, aiyee.

Keep it simple. Base 10/Base 2 will only confuse the poor lads


A nice way to put it would be:
The meaning of a KB is arbitrary. Computer science people could have decided that it should be 633, if they wanted. However, Kilo (under metric, and greek prefixes etc) implies a thousand. So to be nice, they would likely comply with that.

The difference comes as a result of the way computers store their numbers. The infamous "base 2", or binary, or "ones and zeroes", as you may have heard it. The number 1000 can easily and perfectly be represented in base-2(binary). All numbers can. It would not be a good system if they couldn't!

Whats interesting to note is that the number 1000 is significant in "base 10" (regular numbers) in that, it marks the start of an additional digit. 999 uses three, 1000 used four. It's a somewhat natural divider. It's actually what makes the metric system so easy!

However, in binary (using bits, " ones and zeroes") we note that 2 "to the power" 10 = 1024 (Also written as "2 to the exponent 10" or 2^10). We use "2 to the power of" because it is significant in "base 2". Translation: 1024 takes exactly 10bits to represent. This is the "binary" equivalent to "places" in our system. So 1024 is nice because it marks the start/end of a new "place" in the binary system. (Just like 1000 marks the start of a new place in our system)

So computer people could have easily used 1000 as their unit, however, it's not as nice as it doesn't fall right on the edge of a "place" or "digit". 1024 is great, as it takes up exactly 10 binary "digits".

So extending that to the Megabyte, we have: 1MB = 1024KB = 1024B x 1024 =

(Here is the nice part) 2 "to the power" 10 x 2 "to the power" 10 =

2 "to the power" 20.

So a GB becomes 2 "to the power" 30

and so on, and so on...

Just as an aside, to further illustrate why "2 to the power of" is nice in computer math:

You can translate the common metric style units:
1000.
1,000,000.
1,000,000,000.

as

10 "to the power" 3
10 "to the power" 6
10 "to the power" 9

So using 1000 we can make stuff in base10 (our system) look all pretty, where as using 1024 we can make stuff in base2 (computer system) look all pretty and ordered. Obviously, since units of storage, bytes, bits etc, are primarily for computers, it makes sense to structure them in a way that makes *computer math* as ordered as possible.

So there is the "why". The only thing that matters though is that storage manufacturers use 1000, and actual computers use 1024. A stupid inconssistency that only stays around because using the 1000 method makes HDss and DVD sound bigger than they actually are.

Eeeeeeeeevil. Ofcourse, so is describing computer performance in terms of Mhz, but THAT is a whole other can of worms...

Aggies

[SLK001]

There are 4,706,XXX,XXX bytes available on a blank DVD-R disk (where "X" means I don't have the exact number, but they are irrelevant).

Correction: There are 4,707,07X,XXX bytes avail.

[Gil T Pleasure]

Decimal (SI*) multiples: G  = giga = 10^9 = 1,000,000,000 
Binary multiples:        Gi = gibi = 2^30 = 1,073,741,824

A DVD holds 4.7GB (decimal multiples) or 4.38GiB (binary multiples). Disc manufacturers report capacity in decimal multiples, whereas software makers report capacity in binary multiples, but use the SI prefix 'giga,' which is incorrect.

Here's an analogy:
The boiling point of water at sea level is 100 degrees Celcius. It would be correct for me to say that the boiling point of water at sea level is 212 degrees Farenheit. But incorrect if I said 212 degrees Celcius.


*SI = International System of Units

Referrence: http://freedos-32.sourceforge.net/standards.html

[porphyra]

Technically, SI = Le Système International d'Unités

But then, that just being picky, aint it.

[aggies11]

I just like to call it "metric"...

[andydd]

Ha..Vaphun's quote couldnt be any more wrong. Id be somewhat pissed off if my DVD used 400 MB just on 'formatting' !