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-   -   Digital hard copy? (https://www.vintage-radio.net/forum/showthread.php?t=85100)

Big Band Heaven 23rd Jun 2012 2:48 am

Digital hard copy?
 
When I was sat in traffic the other day my mind was wondering.....

music tracks being stored as digital code has been with us for a long time now but just how much data would be contained in say a 2 minute sound file. If all the o's and 1's of the digital code were printed in a book as standard sized print just how much room would it take up?

Would it be the size of a good sized thick book or would it be something like a full set of encyclopedia Britannica's? Any idea anyone?

Amraduk 23rd Jun 2012 3:02 am

Re: Digital hard copy?
 
A 2 minute sound file on a standard CDDA disc would contain:

Samples per second x bit depth x time in seconds = bits.

44,100 x 16 x 120 = 84,672,000 bits!

Your guess is as as good as anyone's on how much space that would take up in printed form. :)

Regards,

Dave.

Big Band Heaven 23rd Jun 2012 3:13 am

Re: Digital hard copy?
 
Dave,
Thanks for doing the basic maths! Using that as a basis and assuming that you could get 50 characters per line and 40 lines to a page (I just picked a novel off the book shelf to work that out) to print that amount of information would take a whopping 42,336 pages! Assuming 500 pages per book then that would be 85 volumes!! Now that would be one hell of a lot of volumes even for just a 2 minute sound file!!

Oh the wonders of miniturisation!!

DragonForce 23rd Jun 2012 3:17 am

Re: Digital hard copy?
 
84 million characters at 6 thousand a page is around 14,000 pages.

I'm taking a guess at 6,000 characters at 10pt per A4 page.....

wireful3 23rd Jun 2012 10:01 am

Re: Digital hard copy?
 
I just did a rough check by looking at the file size of an A4 sheet of 10pt text produced by Appleworks and it was 30Kbytes. I am not very sure about units but I think this is 240,000 bits. I hope I have made a mistake because this does not seem as exciting.

I remember in the very early days of digitising books someone told me it would be possible to get whole encyclopedia on one or two CD ROMs. Perhaps that was a bit optimistic.

As an afterthought Kindle actually does this and stores the books in its memory.

G8HQP Dave 23rd Jun 2012 11:09 am

Re: Digital hard copy?
 
Quote:

Originally Posted by DragonForce
84 million characters at 6 thousand a page is around 14,000 pages.

I thought it was 84M bits? That would be around 10M characters if you had an 8-bit character set with clearly distinguishable characters for each bit pattern. If you just wanted 0s and 1s then you would be using a very inefficient coding method, but one with plenty of redundancy so a garbled character could probably still be read OK: manual/optical ECC!

jjl 23rd Jun 2012 11:24 am

Re: Digital hard copy?
 
The gist of the original question was how much paper would be needed to show the individual bits of a sound file i.e. each printed character would represent a single binary digit and could only be a 1 or 0.

As wireful3 implied, in an 8 bit ASCII text file, each byte can represent one of 256 characters that can be displayed or printed. This gives an 8 fold increase in storage density over printed characters representing a single bit.

Devices such as the Kindle use file formats such as EPUB and PDF to represent books etc. These formats are much more complex than simple ASCII text files, however, they use lossless compression to reduce the file size. This allows several thousand books to be stored in a few gigabytes of FLASH memory.

John

kalee20 23rd Jun 2012 11:45 am

Re: Digital hard copy?
 
It would be far more efficient to have the data printed as hexadecimal. Straight away that's a 4-fold decrease in the number of pages needed.

Incidentally, at one time, one of the companies that I've done work for, required that any ROM contents or microcontroller firmware, be supplied as printed text, just in case. As far as I know, they never had to invoke this ultimate backup...

G8HQP Dave 23rd Jun 2012 12:05 pm

Re: Digital hard copy?
 
There was a time when all computer programs for nuclear power stations had to be supplied on punched paper tape, as that was the only storage mechanism known to be readable over many decades (given proper storage). Magnetic storage was accepted in addition, for convenience.

One could imagine that a modern method would involve some sort of bar code printed on paper tape, as this could give greater bit density.

jjl 23rd Jun 2012 12:32 pm

Re: Digital hard copy?
 
Indeed, 2D barcodes such as the QR codes that seem to be appearing everywhere can encode several kilobytes of data in a small printed area. See here

http://en.wikipedia.org/wiki/QR_code

John

Amraduk 23rd Jun 2012 5:52 pm

Re: Digital hard copy?
 
Hello John,

Quote:

Originally Posted by wireful3 (Post 539285)
I am not very sure about units but I think this is 240,000 bits.

It's actually 245760 bits! 1KB = 1024 bytes, 1byte = 8 bits. I think you've used 1000 = 1KB.

So, 30KB x 1024 x 8 = 245760 bits.

Regards,

Dave.

Amraduk 23rd Jun 2012 6:10 pm

Re: Digital hard copy?
 
The original question was:

Quote:

If all the o's and 1's of the digital code were printed in a book as standard sized print just how much room would it take up?
The book would be full of ones and zeros that represent the value of each bit in the audio file.

It matters not that each character in the book would require a byte to enable it to be printed electronically. If it were typeset by hand using traditional moveable type, you would only require one 'bit' of the alloy from which the type is made (it is composed of lead, tin, and antimony), for each character!

The number of bits in the electronic file needed to print it would, therefore, be 84,672,000 x 8 = 677,376,000 bits, but that wasn't the question!

Regards,

Dave.

Lucien Nunes 23rd Jun 2012 7:02 pm

Re: Digital hard copy?
 
It is alarming to compare the densities and capacities of different storage media. Even different generations of ICs, as predicted by Moore's law, differ in capacity by ratios outside the realm of everyday experience. But when you start to compare optical or modern electronic storage media with historic technologies, the ratios can become laughable.

I have previously thought about the related question: How fast would you have to run 8-column paper tape to play back CD quality audio in real time?

The data rate encoded on a CD is actually 4,321,800 bits/sec. but we don't need as much data for paper tape storage. The 1,411,200 bits/sec of sampled data (44.1k X 2 chans x 16 bits) is subjected to CIRC (cross-interleaved Reed Solomon) error-correction, which increases the rate to 1,881,600 bits/sec. This is a useful feature to retain for paper tape as the high speed is likely to result in damage. You would be able to cut torn ends square and stick them together without interrupting the sound, just as a CD player can read past a small scratch.

Subcodes are then added, which we don't need, followed by eight-fourteen modulation. This is useful for the serial optical system as it makes the signal self-synchronising and reduces bandwidth (despite increasing the number of symbols stored). However we don't need it for paper tape as this has sync holes and stores at byte-width. Nor do we need the sync word added at the final stage.

So the data rate of 1,881,600 bits/sec is written to tape with 8 bits/byte and 10 bytes/inch. The necessary tape speed in MPH is therefore:
1,881,600 / 80 / 12 / 5280 * 3600 = 1336 MPH.
For a visualisation of this, consider a car driving along the motorway at 67 MPH with 20 tapes tied on to its rear bumper, all being read at once. 20 parallel tapes would be clumsy; you might consider one tape per channel, running at 668 MPH. This has the advantage of being slightly below the speed of sound.

An interesting point - the linear density of audio storage on tape is close to that of the air between speaker and listener. If you sit eight feet from the speaker, about seven feet of tape's sound capacity is in acoustic transit from driver to eardrum.

I leave as an exercise for the reader, the computation of the mass of stone tablets of ordinary construction required to store the contents of a 32GB memory stick.

Lucien

Amraduk 23rd Jun 2012 9:12 pm

Re: Digital hard copy?
 
I forgot to take into account the fact that there are two channels on a CD, so my figures need to be doubled! I didn't take into account any error correction or other 'housekeeping' performed by the CD player, as it was only the resulting audio that was of interest.

Regards,

Dave.

Amraduk 23rd Jun 2012 9:17 pm

Re: Digital hard copy?
 
Quote:

Originally Posted by kalee20 (Post 539307)
It would be far more efficient to have the data printed as hexadecimal. Straight away that's a 4-fold decrease in the number of pages needed.

Be that as it may, it was how much space would be taken up by the value of every bit of the audio file being printed in a book. There was no requirement for efficiency!

Regards,

Dave.

Amraduk 23rd Jun 2012 9:24 pm

Re: Digital hard copy?
 
Hello Dave,

Quote:

Originally Posted by G8HQP Dave (Post 539301)
I thought it was 84M bits? That would be around 10M characters if you had an 8-bit character set with clearly distinguishable characters for each bit pattern.

The requirement was for the value of each bit to be printed in a book, as ones and zeros. That's a single 'character' per bit - as I said in a previous post: One 'bit' of the alloy from which moveable type is made, so each printed 'character' represents one bit of the audio file.

Regards,

Dave.

DragonForce 23rd Jun 2012 10:41 pm

Re: Digital hard copy?
 
Quote:

Originally Posted by G8HQP Dave (Post 539301)
Quote:

Originally Posted by DragonForce
84 million characters at 6 thousand a page is around 14,000 pages.

I thought it was 84M bits? That would be around 10M characters if you had an 8-bit character set with clearly distinguishable characters for each bit pattern. If you just wanted 0s and 1s then you would be using a very inefficient coding method, but one with plenty of redundancy so a garbled character could probably still be read OK: manual/optical ECC!

Yeah, that would be true - but the OP wanted to print it out as binary, so 84 megabit is still 84 million characters - each bit being 1 or 0.

If you printed it out as hex, then the numbers change - 8 bits to a byte, each byte being represented by a two digit number 00 - FF (0 to 255 in decimal).

If you then take the 10 million characters and represent as hex, you're looking at printing 20 million characters, assuming you don't need a separation character between the values (a "," say). Even at 20 million characters, you're still looking at a huge amount of printed paper.

jenkinsrichard 27th Jun 2012 8:27 pm

Re: Digital hard copy?
 
You could always use a very small font for the ones and zeros.

Big Band Heaven 28th Jun 2012 6:17 am

Re: Digital hard copy?
 
Thanks for all these comments. THe purpose of my original post was to get a handle on just how much data was contained in a standard 2 minute sound file on a CD and what this would look like at a standard sized rather than as microscopic pits burned on to a CD. The sheer amount of paper needed to print out that amount of binary code or even as hex code is quite staggering. Now I wonder how much code is contained in two minutes of video on a blue ray disk.

Radio Wrangler 28th Jun 2012 6:39 am

Re: Digital hard copy?
 
Another interesting size ratio occurs with photography. Consider the area of a sensor collecting light. Take a few hundred shots and compare the area of CDROM or DVD it takes to store them on, and this is an optical to optical comparison.

It illustrates the difference in densities and the effects of coding, even if you're not using lossy compression.

David


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