Re: Partition Problems w/ 810mb HD

[cmcmanis@scndprsn.Eng.Sun.COM (Chuck McManis)]

You know its one thing to read about how history of things gets twisted
to sort of explain how things are or could be. Its another to experience
it in real time :-)

>I think there might be some (alot of!) confusion here with respect to the
>disk size discussion...

No kidding!

>1) One million bytes is ALWAYS equal to 1 Megabyte... let's not
>   rewrite the math books to fit the problem! 

Uh-oh we've started out with something of a faux pas now. The crux of
this silly discussion was the prefix 'Mega' which has, for several
centuries meant units of 1,000,000. However, there are those pesky
engineers who built a memory chip (the 2112 if memory serves) that
could address 2^10 bits. Now 2^10 happens to be 1024 distinct bits,
and those pesky engineers got _really_ tired of calling these thing
1024 bit memories (although they did for a long time.) and then some
unspoken agreement was made to shorten multiples of 1024 to be "K"
since that was easier to type and we all knew what we were talking
about anyway. Of course, the engineers didn't make a global change,
no they didn't start calling 1024 ohm resistors "1K resistors" or
make 1/1024th of a volt a millivolt. No, they realized that they
could use the term 'K' in context and keep it straight.

This got to be a habit, and a bad one at that.

Next came memories that could address 2^20 bits. Now technically this
was 1024 * 1024 and really that was 1,048,576 bits but since we're calling
1024 a Kilobit, 1024 Kilobits could reasonably be called 1 Megabit right?
Sure, as long as its just between us propellor heads and we never get
them confused with the "real" definition of Mega which is 1,000,000.

Now we start adding magnetic media, which have a storage capactity that
is not dictated by the binary number system, but by the physical space on
the magnetic media and the ability of the electronics to distinguish bits.
So technically we (being the engineers) could drop this silly convention
of 1K = 1024, 1M = 1024 * 1K, and 1G = 1024 * 1M. After all, the disk
isn't memory, is it? Ah but there is the rub, in a way it is memory with
a very slow access time. Also if you are already talking about memory
using these altered units then if you discuss the disk in the same
units you don't have to figure out if your program that takes 4K of
core memory will fit in 4K bytes on the disk. 

And so the habit was continued and it really was just a convention, a
bogus one, but convienient.

But the engineers ran up against a problem, and that was "Marketing".
And worse we exceeded that magic size of "twenty" megabytes. You
see engineers had no reason to change what was going on because after
all we all _knew_ that 20M was 20 * 1024 * 1024 or 20,971,520 bytes
and of course if your truncate to the nearest million 20M is 20M right?
but a 21 megabyte drive (anyone remember the Seagate 225?) was
22,020,096 bytes. Hmm, so those pesky marketeers over in Microscience
or whereever it was they were trying to unseat the Shugart/Segate monopoly
on hard disks, got the bright idea that they could advertise these things
as 22M drives (* M = 1,000,000). Now would you rather have a 21M or a 22M
drive? Obviously the 22M one is bigger right? wrong. They are exactly the
same size, and this strategy fell flat on its face and these marketeers
got roasted soundly by the engineering community. 

Anyway, the idea comes and goes (much to the annoyance of folks who don't
care which way it goes as long as everyone uses the same notation.) and
didn't really take hold until people like my Mom started walking into
computer stores to buy a computer. She _doesn't_ know that the 22M drive
is the same size as the 21M drive and so she goes for the "bigger" drive
at the same price. Bam! Hooked one. Now the practice has become common
place.

>2) If the drive were actually 810 Megabytes large instead of 810 Megabits
>   then that would be equal to  8 * 810 * 10**6 = 6480 * 10**6 = 6480 Megabits
>   (which btw = 6.48 Gigabits) If it's 810 Megabits, then that's equal to
>   (810/8) * 10**6 = 101.25 Megabytes. Either way, it doesn't add up to 770
>   or 772...

The drive is in fact has the ability to store 810,549,248 bytes of data.
That can be computed by multiplying their 
    cylinders * tracks * sectors * bytesPerSector.

The engineers divide that by 1024 * 1024 and get 773 Megabytes. The marketeers
divide it by 1,000,000 and get 810 Megabytes. Either way its a lot but using
the marketing way you get 37 million bytes for "free". 

>   Just to clarify further, disc sizes are usually give in Megabytes. 
>   The abbreviations are supposed to be: MB = Megabytes and Mb = Megabits
>   but these are often confused.

Actually to be perfectly clear, the unit Megabits is typically used
in semiconductor memories (makes them sound larger) and communication
channels. Disks are always rated in bytes (kilo or mega). Typically
disks with kilo byte ratings are using the notion that 1 kilo = 1024 bytes.

As an interesting aside, the "1.44M" floppy disk gets its unit by its
ability to hold 80 tracks of 18 sectors, each containing 1024 bytes.
Multiplied out that is 1,474,560 bytes (or 1.475 Mb in marketing speak)
but divided by 1024 you get 1440 Kbytes or 1.44 Mbytes. In this case
the M stands for 1000 * 1024 bytes! Pretty wild yes?

>3) Although physical memory and disk sizes are actually configured in binary
>   increments, i.e. 2**10 = 1024, they are commonly rounded off to the nearest
>   decimal multiple of K or M bits or bytes. But this is only a ROUNDOFF 
>   issue, and generally the roundoff is in the downward direction, i.e.
>   10 Megs is really 1,024,000, 16 K is really 16,384 etc..

Not exactly. Four megabytes of memory is addressable with 22 binary bits.
Unlike disks if you swap the units around on memory you don't sell any.
22 bits = 4,194,304 bytes. 

>4) So where did all that disk space (810 - 770) actually go?  The key phrase 
>here was:
>"After formatting the drive..."
>Yep, that's the byte eater... the formatting process automatically reserves 
>alot of space for administering the file system, for spare tracks, etc.
>typicallly 10% or more of your brand new disk! Bummer...

And this one really stunned me. The drive capacity is 810,549,248 bytes
FORMATTED. This is mythos is left over from another marketing trick which
was to give the raw capacity of the drive. This was calculated using the
number of tracks per inch the stepper could resolve and the linear bit
density the read/write heads could distinguish. But the bits on the disk
included synch bits, gaps between sectors to allow the electronics to
recover, etc. And it was during that period where raw capacity was the
number quoted and formatted capacity was in the footnote. For what its
worth the raw capacity of those "1.44M" 3.5" disks is 2 megabytes but
you can't get two megabytes without changing their format. These days
in the world of SCSI and IDE hard disks the computer has no idea how
to format the drive, it just knows how many "blocks" it can store on 
the drive and how big a block is. Thus for all intents and purposes
the unformatted capacity is irrelevant and no longer used in the
literature.

--Chuck McManis