Answering Common Data Storage and Downloading Questions

An odd thing happens on the way through the public school system to the University. Some students—far too many, actually—are led through peer interactions and other subtle influences to believe that they are "not good at math." Actually, no one is "good at math" to start with. To become good at anything requires learning about that thing, whether it is competing in sports, mastering a musical instrument, becoming a good writer, accomplishing photographic competence, or gaining confidence in math, through practice. We know you can do these sorts of data storage and downloading calculations. Let's practice!

In each of the following questions, attempt to answer the question before looking at the provided answer. The questions are given in pairs, so if you don't obtain the correct answer for an odd-numbered question, study the answer and then attempt the even-numbered question immediately following, as it will be of the same type.

Practice makes perfect, or at least passable. It is OK to use a calculator to do necessary calculations, as long as you understand how the calculations are done. It is also OK to make mistakes. Indeed there may be some errors in the answers given below, so carefully scrutinize your answers with the given ones.

Test Yourself

1. Suppose you have an Internet connection that provides you with an average download speed of 4Mbps. How many bytes per second can be downloaded with this connection speed?

Reveal Answer

We remember that there are 8 bits in every byte. A download speed of 4Mbps (4 million bit per second) will result in 4,000,000 bits being downloaded per second. To compute the number of bytes represented in 4,000,000 bits, we must divide 4,000,000 by 8, yielding 500,000 bytes per second. We can summarize the arithmetic as:

4Mbps = 4,000,000 bits per second

4,000,000 bits per second/8 bits per byte = 500,000 bytes per second.

 

2. Suppose you have an Internet connection that provides you with an average download speed of 1.5Mbps. How many bytes per second can be downloaded with this connection speed?

Reveal Answer

We remember that there are 8 bits in every byte. A download speed of 1.5Mbps (1.5 million bits per second) will result in 1,500,000 bits being downloaded per second. To compute the number of bytes represented in 1,500,000 bits, we must divide 1,500,000 by 8, yielding 187,500 bytes per second. We can summarize the arithmetic as:

1.5Mbps = 1,500,000 bits per second

1,500,000 bits per second/8 bits per byte = 187,500 bytes per second.

 

3. Suppose you have a download speed of 1Mbps and you are downloading a 5MB picture file. How many seconds will it take to download the file. Explain how you arrived at your answer.

Reveal Answer

40 seconds. A download speed of 1Mbps means that one million bits will download in 1 second. The file size of the picture is 5MB, which means that the file contains 5 million bytes. Since there are 8 bits in a byte, the number of bits in the picture file is thus 40 million.  Given that the download speed is one million bits per second, the download will take 40 seconds. The arithmetic is:

Number of bytes in the 5MB picture file is 5,000,000

Number of bits in the 5MB picture file is thus 8*5,000,000 = 40,000,000

The download speed of 1Mbps = 1,000,000 bits per second

So, the time to download the 5MB picture file is

 (40,000,000 bits) / (1,000,000 bits per second)

= 40/1 seconds

= 40 seconds.

 

4. Suppose you have a download speed of 3Mbps and you are downloading a 4MB picture file. How many seconds will it take to download the file. Explain how you arrived at your answer.

Reveal Answer

10.7 seconds. A download speed of 3Mbps means that three million bits will download in 1 second. The file size of the picture is 4MB, which means that the file contains 4 million bytes. Since there are 8 bits in a byte, the number of bits in the picture file is thus 32 million.  Given that the download speed is three million bits per second, the download will take 10.7 seconds. The arithmetic is:

Number of bytes in the 4MB picture file is 4,000,000

Number of bits in the 4MB picture file is thus 8*4,000,000 = 32,000,000

The download speed of 3Mbps = 3,000,000 bits per second

So, the time to download the 4MB picture file is

 (32,000,000 bits) /(3,000,000 bits per second)

= 32/3 seconds

= 10.7 seconds (rounded up).

 

5. Suppose you have a download speed of 1Mbps and you are downloading a 500KB picture file. How many seconds will it take to download the file. Explain how you arrived at your answer

Reveal Answer

4 seconds. The picture file size is  500,000 bytes. There are 8 bits in a byte, so there are 4,000,000 bits in the picture file.  The download speed is 1,000,000 bits per second, so it will take 4 seconds for the download to happen. The arithmetic is: 

(8*500,000 bits) / (1,000,000 bits per second)

= (4,000,000 bits) / (1,000,000 bits per second)

= 4 / 1 seconds

= 4 seconds

 

6. Suppose you have a download speed of 3Mbps and you are downloading a 900KB picture file. How many seconds will it take to download the file. Explain how you arrived at your answer

Reveal Answer

2.4 seconds. The picture file size is 900,000 bytes. There are 8 bits in a byte, so there are 7,200,000 bits in the picture file.  The download speed is 3,000,000 bits per second, so it will take 2.3 seconds for the download to happen. The arithmetic is: 

(8*900,000 bits) / (3,000,000 bits per second)

= (7,200,000 bits) / (3,000,000 bits per second)

= 72/30 seconds

= 2.4 seconds.

 

7. Suppose you are in the business of creating feature-length movies that you record to Blu Ray discs for distribution, and that the size of your movies is on average 20GB. Your plan is to keep master copies of these movies on an external hard drive. How many master movies could you store on a 2TB external hard drive?

Reveal Answer

To arrive at the answer we must divide 2TB by 20GB. That is, we must perform the division:

(2,000,000,000,000 bytes)/(20,000,000,000 bytes per movie)

Canceling the 0's in the denominator with the numerator yields

(200/2) movies = 100 movies

If you keep your entire movie projects—including the original raw footage plus different versions of your movies—on this external hard drive, you will be able to hold far fewer than 100 movies. Movies eat up a lot of storage space.

 

8. Suppose you are a graphics designer or artist and that you have created works by hand that you digitize for posterity by using a flatbed scanner and/or a camera and that the average size of the resulting digitized masters is 25MB. Suppose now that a potential client want some of your digitized work for review. You plan to send the requested copies on a USB thumb (flash) drive. You find an old 4GB thumb drive for this purpose. How many of your digitized masters can you fit on this USB thumb drive?

Reveal Answer

To arrive at the answer we must divide 4GB by 25MB. That is, we must perform the division:

(4,000,000,000 bytes) / (25,000,000 bytes per master)

Canceling the 0's in the denominator with the numerator yields

(4,000/25) masters = 160 masters

 

9. Suppose you have a camera that stores its files on a memory card. Suppose further that you buy a 16GB memory card for use in that camera. Past experience has shown that if you take pictures at their full resolution the picture file sizes are about 15MB each. How many pictures can you take before the memory card gets full (assuming you don't delete any of the pictures along the way)?

Reveal Answer

To arrive at the answer we must divide 16GB by 15MB. That is, we must perform the division:

(16,000,000,000 bytes) / (15,000,000 bytes per picture)

Canceling the 0's in the denominator with the numerator yields

(16,000 / 15) pictures = 1,066 pictures

 

10. Suppose you have a movie camera that stores its files on a memory card. Suppose further that you buy a 16GB memory card for use in that camera. Past experience has shown that your movie clips are on average 25 seconds long, and that the camera records movies at 32Mbps. How many movie clips can you take before the memory card gets full (assuming you don't delete any of the clips along the way)?

Reveal Answer

To arrive at the answer we must first convert the various quantities to the same measures. We note that the movie card can hold 16 gigabytes, that is, 16,000,000,000 bytes, of data. The camera records the movie clips at 32Mbps, which is 32,000,000 bits per second. Dividing that value by 8 calculates that the camera records 4,000,000 bytes per second. The number of bytes required to store a 25 second movie is 100,000,000, or 100MB. We can thus record 160 movie clips of 25 seconds each on a 16GB card. The arithmetic is as follows:

Movie recording speed in bytes = (32,000,000 bits per second) / (8 bits per byte)

= 4,000,000 bytes per second

Number of bytes in a 25 second clip = 25 seconds * 4,000,000 bytes per second

= 100,000,000 bytes

Number of 25 second clips that can be stored in 16 gigabytes  

= (16,000,000,000 bytes) / (100,000,000 bytes per clip)

= 160/1 clips (by canceling 0s)

= 160 clips