Calculating CD Requirements for a 39-Hour Music Collection

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In summary, the conversation discusses the process of recording a collection of music and determining the number of CDs needed. It is mentioned that the music is 39 hours long and will be encoded using MP3 at a rate of 128kb/s. It is also noted that a CD can store up to 700 MB of information. Through calculations, it is determined that 13 CDs will be needed to store the entire collection. There is also a discussion about the difference between bits and bytes and how it relates to computer storage and network speeds.
  • #1
justagirl
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What am I doing wrong in this problem?

You need to record an entire collection of your favorite music. It consists of 39 hours of music. Assuming you are using MP3 encoding (MPEG Audio Level III at about 128kb per second), how many CDs will you need? (hint: a CD can store up to 700 MB of information.)

I did: 128 kb/s * 3600 * 19 = 8755200 kb (to be coded)
Compression ratio: 8 (?)

8755200 * 8 = 70041600 kb (to be coded on CD)

One CD can store: (700 MB) = (700) * (2^10) kB * 8 = 5734400 kbits

# of CDs needed = 8755200 / 5734400 = 13 CDs.

Thanks!
 
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  • #2
Where did the 19 in the first line come from? Or is it 19hrs instead of 39hrs?

In the CD figuring line, you need 2^20 for a MB and then you'll come up with a realistic number of bits that can be stored on a CDROM.

Note sure where you're getting your 8 from but I'll explain mine.

Ok, you need to be really careful about lower-case b and upper case B since they mean different things in the world of computers. It seems you have a bit of understanding on this but I'll re-iterate to make sure.

b = bit = 0 or 1
B = byte = 8 bits

Its far worse than the typical truth-strecthing where manufacturers use base 10 numbers (1MB = 1,000,000 Bytes) and software uses base 2 numbers (1MB = 1,048,576 Bytes).

The difference between bits/bytes becomes most obvious when you use networks where the bits is a dominant measure, like a modem connection that is 44kb/s (kilo-bits with little b) where you download files at maybe 5kB/s (kilo-Bytes with big B) as reported in the software.

I've double-checked my math with a few MP3 files I have on my computer, compressed them myself off my CDs so I assume they are accurate.

128 kb/s * 3600 seconds = 460,800kb/hr / 8 bits = 57,600kB/hr

I come up with just a shade more than 12 hours per 700 MB capacity CDROM. I'll let you complete your own math for your example. :smile:
 
  • #3


There are a few errors in your calculation. First, you have multiplied by 19 instead of 39, so your total amount of music to be coded is incorrect. Additionally, the compression ratio for MP3 encoding is typically around 10:1, not 8:1. And finally, you have used 3600 seconds instead of 3600 seconds * 39 hours, which would give you the total number of seconds in 39 hours.

To correct the calculation, it should be:

128 kb/s * 3600 seconds * 39 hours = 17971200 kb (to be coded)

Compression ratio: 10

17971200 * 10 = 179712000 kb (to be coded on CD)

One CD can store: 700 MB = 700 * 2^10 kB * 8 = 5734400 kbits

# of CDs needed = 179712000 / 5734400 = 31 CDs

Therefore, you would need 31 CDs to store your entire 39-hour music collection.
 

What is simple compression and how does it work?

Simple compression is a process of reducing the size of a file or data by removing redundant or unnecessary information. This is achieved by using algorithms that identify patterns in the data and replacing them with shorter representations. The compressed file can then be decompressed to its original form using the same algorithm.

Why is compression important?

Compression is important because it allows for efficient storage and transmission of data. By reducing the size of a file, it takes up less space on a storage device and can be transmitted faster over a network. This is especially useful for large files such as images, videos, and documents.

Is simple compression lossless or lossy?

Simple compression can be either lossless or lossy, depending on the algorithm used. Lossless compression retains all the original data after decompression, while lossy compression sacrifices some data to achieve a higher compression ratio. Lossless compression is preferred for data that cannot afford to lose any information, while lossy compression is more suitable for multimedia files where minor losses in quality are acceptable.

What are some common compression algorithms?

Some common compression algorithms include ZIP, RAR, and GZIP for general data compression, and JPEG, MP3, and MPEG for image, audio, and video compression, respectively. Each algorithm has its own unique features and characteristics, making them suitable for different types of data.

Can compressed files be further compressed?

Yes, compressed files can be further compressed. However, the amount of compression achieved may not be significant as the first compression has already removed most of the redundant data. Attempting to compress already compressed files may also result in a loss of quality or even corrupt the file.

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