How can I figure this out?

Question

I'm a bit confused. Please help. :) 

This is the problem: 

A byte is not an official SI unit, but it is often used to describe digital information as if it were a metric unit. For example, you may have an iPod that can accommodate 8 gigabytes of music. If you and your friends combine the information capacity of all of your Ipods and an external hard drive, how many songs would you have if the average file size is 4,000 kb? The capacity of the iPods and the external hard drive is listed below. 

• iPod Nano- 8 gigabytes
• iPod Nano- 16 gigabytes
• iPod Classic-160 gigabytes
• iPod Touch-64 gigabytes
• External Hard drive- 1 terabyte

Answer 1

A byte is normally one piece of information. 

At the start of computers one byte was 8 bits of binary data which gave them the ability to store 256 bits of data,so it could represent all the numbers and alphabet plus others.

Since all computers store data as binary the definition of a kilobyte instead of being 1000 bytes is actually 1024 bytes or

2¹⁰ bytes.

so:

1 megabyte would be 1024 x 1024 or 2²⁰ bytes or 1,048,576 bytes

1 gigabyte would be 1024 x 1024 x 1024 or 2³⁰ bytes or 1,073,741,824 bytes

1 terabyte would be 1024 x 1024 x 1024 x 1024 or 2⁴⁰ bytes or 1,099,511,627,776 bytes

Also every device's capacity is sometimes a close approximation  or refers to unformulated capacity since the format process takes available data.

All that being said to answer your question:

 

iPod Nano would hold (8*1024*1024)/4000 = 2097 songs

iPod Nano would hold (16*1024*1024)/4000 = 4194 songs

iPod Classic would hold (160*1024*1024)/4000 = 41,943 songs

iPod Touch would hold (64*1024*1024)/4000 = 16,777 songs

1 terabyte hard drive would hold (1024*1024*1024)/4000 = 267,435 songs

 

Or as can be calculated from the above 262 songs per gigabyte based on a 4000 kilobyte average size.

 

 

Answer 2

Hi Gaby,

 

I was an electrical engineering student back in the days where computers used vacuum tubes and took up huge, very cold rooms.  In that day, a "byte" was 8 "bits".  A bit is a single line (a wire) that carries either a 1 (a positive DC voltage, usually 5V) or a 0 (electrical ground).  And believe it or not, all of our digital, electronic gadgets that we use, when it is all boiled down, run on just 2 numbers:  1 and 0.   So there is the background.

 

I think what your Geology teacher is getting you to work with is all of the prefixes.  

 

1 gigabyte = 10⁹ bytes.

1 kilobyte (kb) is 10³ bytes

1 megabyte is 10⁶ bytes

1 terabyte is 10¹² bytes

 

 

1 song = 4000 x 10³ bytes or 4 x 10⁶ bytes or 4 Megabytes

 

iPod Nano :  8 x 10⁹ Bytes/(4 x 10⁶ Bytes per song) = 2000 songs

 

iPod Nano :  16 x 10⁹ Bytes/(4 x 10⁶ Bytes per song) = 4000 songs

 

iPod Classic:  160 x 10⁹ Bytes/(4 x 10⁶ Bytes per song) = 40,000 songs

 

iPod Touch: 64 x 10⁹ Bytes /(4x10⁶ Bytes per song) = 16,000 songs

 

External Hard Drive:  1 x 10¹² Bytes/(4x10⁶ Bytes per song) = 250,000 songs.