Lotta Yotta

Hi, group. I am a newbie here and wanted to get some opinions on a 'puzzle' of sorts that I made up over the past few days. It really turns out to be fairly simple Geometry, but I thought I'd post it and see what everyone thinks. Constructive flames are welcome. Enjoy!

Business Week states that, 'In ten years, the volume of online data accessible either on the Internet or on corporate networks is expected to approach a yottabyte...'

Currently, the largest named measure of data is the yottabyte (Y, which is exponentially greater than the zettabyte, exabyte, petabyte, terabyte, and so on. The yottabyte is approximately equal to 5X * 10^6, where X is equal to all printed matter that exists on our planet. You're on your own for finding the definitive measure of a yottabyte.

The highest-density digital tape (which is the highest-density medium currently in common use) made by one of the world's leading manufacturers stores data at a density of 124K bpi.

At a tape thickness of 8.9 microns, what must the diameter of a roll of tape be in order to store one YB of data, assuming that it is wrapped around a spool with a diameter of 0.5 inches and assuming that there is no space between the layers of tape?

Is that a base-10 or a base-2 K?

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1675 kilometers. (Saw one advertised at Ebay?)

You've asked the wrong question, I think. K=10^3 vs. K=2^10 is only a 2.4% difference, less than one part in eighty. But yotta=10^24 vs. yotta=2^80 is a 21% difference, more than one part in five.

I'm certain a yotta is 2^80, and 10^24 is only an approximation. I'm not sure about the K's and megs in storage devices.

For example, one of my drives is advertised at 2.55 gigs, but my computer says it has 2.38 gigs. Another is advertised at 2.3 gigs, but my computer says it has 2.12. Obviously, my computer counts a gig as 2^30, while the disk manufacturer uses 10^9.

The confusion is not from tera...yotta, etc which are defined as respective powers of ten.

The confusion is that 1KB is defined a 1024 bytes. Thus when the standard suffixes are used with-BYTE, the different rules apply.. thus a gigabyte is 2^30 Bytes, but a gigabuck is still 10^9 dollars and a gigaHertz is still 10^9 Hertz.

RJ Pease

When you're buying a hard disk, the advertised gigabyte may be 10^9. That's why I am uncertain whether the specs of a tape drive are in k's of 10^3 or 2^10.

If they use shorthand as 10^9 for gigabytes, they are wrong.

By agreement 1GB= 2^30 bytes or 1,073,741,824 actual bytes . you get a 7% discrepancy.from Actual bytes.

In the cases you cited, the decimal number of bytes is always larger than the MB,GB rating. the advertisers give the decimal bytes, because it LOOKS like more.

(as an aside, they are prone to hype the specs . For a while, they used to quote peak to peak voltage gain as 'Power' when rms was the accepted standard, as a result, it 'LOOKED' about three times as 'Powerful' to a non-techie out to impress his friends )

For example, one of my drives has 2,142,564,352 actual bytes, but the COMPUTER rates it at 1.99GB . A merchandiser advertising it a 2.14 GB would be WRONG, but if he said it had 2.14 'actual gigs' this would be misleading but technically true.

The reason for this strange convention is that when allocating memory and other stuff, the calculations are displayed in Hex which is strongly related to binary, it's to 'Look at' for the programmer than in decimal.

Since you are working in bytes ,the power of two rule applies to the total number of bytes. it always goes up by powers of two. thus 1 Mb = 1024 Kb. 1 Gb= 1024 Mb, etc.

The terms Giga, Mega, etc are abused by agreement (or by default to nerds) , but only for bytes, as far as I know, even for BITS, the power of ten conventions apply.

RJ Pease

Who is bound by this agreement? If the manufacturer may have meant 10^9, why should I assume he meant 2^30?

Voltage gain? That's not power unless you know the input voltage and the output impedence.

With a sine wave, peak power is twice rms, IIRC. A nerd might want to think in peaks because that represents the potential for blowing a tweeter. I think you're right that they used to talk about p-p power, but the concept seems mythical to me.

How about horsepower? Brake horsepower is analogous to RMS. A lot of manufacturers use theoretical calculations, which are like peak-to-peak power.

What's an actual gig? At one time a gig was a two-wheeled carriage. We used to call soapbox racers gigs.

What would specifying memory in base 1024 (2^10) have to do with programming in base 16 (2^4)?

Years ago I worked with minicomputers: 16-bit bytes (we called them words) and 10-bit addressing. So the convention of counting memory in units of 1024 goes back more than 30 years. We programmed bit by bit and for convenience wrote in octal. The machine didn't care about octal. It was just easier to write and speak than binary.

We used k's of 1024 for memory because the machine addressed memory in binary.

We used holerith cards, paper tape, and magnetic tape for mass storage. The machine didn't address mass storage at all. A file was however long it needed to be, and there was no point in expressing its length in binary. So if disk manufactures use decimal gigs, they are following a long tradition.

That's powers of 1024.

As a matter of fact, we seem to be talking about bits. The spec was 124K bpi. Of course, it's easy to confuse B and b, which is a reason it was safer in the old days to say 'words' instead of 'bytes'.

I'm not entirely convinced that is the case.

When you buy a hard disk, the advertised capacity will be the *unformatted* capacity. This includes things like sector addressing information, intersector gaps and spare tracks, all of which are unusable for storing real data. That accounts for somewhere between 5 and 10 percent of the advertised disc space.

I looked up Megabit on Goolge Glossary, and most of the definitions say it's 1,048,576 bits. One says 'a million', some say 'about a million', one says '100,000 characters' (I guess they've included one start bit and one stop bit for each byte). One of the definitions says:-

1) In terms of data transfer, one megabit per second (Mbps) refers to 1,000,000 bits of information transferred per second. 2) In relation to data storage, one megabit is exactly equal to 1,048,576 bits of stored data.