Digital download and file storage Syllabus: FSCo2 Focus Study: Mathematics and Communication

Digital Storage

b A bit is the basic unit for storing electronic data, for example an MP3 file. The term bit is a shortened form of binary digit.

A bit stores the value of 0 or 1. The abbreviation for bit is b.

B A byte is equal to 8 bits. In a computer, one byte is used to store a character. For example the letter a is stored as 01100001. The abbreviation for byte is B.

Bits vs Bytes as Fast As Possible http://gomaths.net/3370 3:07 onwards is an advertisement.

1 byte (B) = 8 bits (b)

Example

A. Convert 255 bytes to bits. From the Data Sheet, 1 B (byte) = 8 bits. So, 255 bytes in bits must be 8 times larger.

255 B = 255×8 b= 2040 b

Exercise

1. Convert 560 bytes to bits.

560 B = _____×8 b= _______ b

2. Convert 960 bytes to bits.

B. Convert 7200 bits to bytes. From the Data Sheet, 1 B (byte) = 8 bits.

So, 7200 bits in bytes must be 8 times smaller or !! the size. Therefore, divide.

7200 b = 7200 ÷8= 900 B

3. Convert 1200 bits to bytes.

1200 b = _____÷8 = _______ B

4. Convert 984 bits to bytes.

Units of storage These units of storage are given in the HSC Examination Formulae and Data Sheet.

Unit Relationship

1 byte 1 B = 8 bits

1 kilobyte (kB) 1 kB = 1024 bytes

1 megabyte (MB) 1 MB = 1024 kB

1 gigabyte (GB) 1 GB = 1024 MB

1 terabyte (TB) 1 TB = 1024 GB

Convert units of storage

× 1024 × 1024 × 1024 × 1024

B kB MB GB TB

÷ 1024 ÷ 1024 ÷ 1024 ÷ 1024

Example

C. Convert 8 MB to kilobytes. From the Data Sheet, 1 MB = 1024 kB. So, 8 MB in kilobytes must be 1024 times larger.

8 MB = 8×1024 kB= 8192 kB

5. Convert 4 GB to MB.

4 GB = _____×1024 MB= _______ MB

6. Convert 7168 kB to bytes.

D. Convert 3072 kB to megabytes. From the Data Sheet, 1 MB = 1024 B. So, 8 MB in kilobytes must be 1024 times smaller. Therefore, divide.

3072 kB = 3072 ÷1024 MB= 3 MB

7. Convert 4608 GB to TB.

4608 GB = 4608÷1024 TB= 4.5 TB

8. Convert 7168 kB to bytes.

DATA SHEET

Size and Storage

E. A music file (MP3) is about 6 MB. Approximately how many songs can be stored on a 2 GB MP3 player? From the Data Sheet, 1 GB = 1024 MB.

2 GB = 2×1024 MB= 2048 MB

We need the number of 6 MB files that fit on a 2048 MB (2 GB) player. Mathematically, this means how many 6’s go into 2048. Therefore, divide.

Number of songs = 2048÷ 6= 341.333...≈ 341 songs

9. A photo taken on a particular phone uses about 1.8 MB of memory. There are 4 GB of space available on the phone. How many photos can be taken and stored? From the Data Sheet, 1 GB = 1024 MB.

4 GB = 4× ______ MB= _______ MB

We need the number of 1.8 MB files that fit in 4096 MB (4 GB).

Number of photos = _______÷ ____= _______≈ _______ photos

10. Kayla makes a 5-minute phone call via Skype at 1 MB per minute. How many kB did she use?

To see a comparison of data size, view this infographic http://gomaths.net/3395.

Think, why should you round the calculated answer down?

Download Speed The rate at which information is downloaded onto your computer is usually measured in bits per second (bps) or kilobits per second (kbps). 1 kilobit = 1000 bits.

Download speed = Data

Time

F. It takes 50 mins and 25 seconds to download a video file of 318 MB. Calculate the download speed correct to the nearest kbps. We first change the file size to bytes.

318 MB = 318×1024×1024 bytes=333 447 168 bytes

Then convert to bits.

= 333 447 168×8 bits= 2 667 577 344 bits

Then convert to kilobits.

= 2 667 577 344 ÷1000 kilobits= 2 667 577.344 kilobits

Convert the time to seconds.

50 mins 25 seconds = 50× 60+ 25 seconds= 3025 seconds

Download speed = DataTime

= 2 667 577.3443025

= 881.843...= 882 kbps

11. Find the download speed in kbps for each of the following. Round answers to the nearest kbps. A 6 MB song downloads in 2 minutes.

6 MB = 6× _____× _____ bytes= 6,291,456 bytes= 6,291,456× _____ bits= 50,331,648 bits= 50,331,648÷ _____ kilobits= __________ kilobits

2 min = 2× _____ seconds= _____ seconds

Download speed = DataTime

=

= __________ kbps≈ _______ kbps

This is the amount of data.

This is the time taken in seconds.

Convert to bytes.

Convert to bits.

Convert to kilobits.

First, calculate the amount of data in kilobits.

Second, convert the time to seconds.

Finally, calculate the download speed.

12. A 7.5 MB file downloads in 10 seconds.

G. Find, correct to the nearest second, the time taken to download a 4.5 MB song at a speed of 1000 kbps. Need to change 4.5 MB to bytes.

4.5 MB = 4.5×1024×1024 bytes= 4 718 592 bytes

Then convert to bits.

= 4 718 592×8 bits= 37 748 736 bits

Then convert to kilobits.

= 37 748 736 ÷1000 kilobits= 37 748.736 kilobits

Time = DataSpeed

= 37,748.7361000

= 37.748...≈ 38 s

13. Find the time taken, correct to the nearest second, for the following downloads. A 8 MB song at 100 kbps.

8 MB = 8× _____× _____ bytes= 8,388,608 bytes= 8,388,608× _____ bits= 67,108,864 bits= 67,108,864 ÷ _____ kilobits= __________ kilobits

Time = DataSpeed

= 100

= __________≈ ______

This is the amount of data.

The speed was given in the question.

Convert to bytes.

Convert to bits.

Convert to kilobits.

Calculate the amount of data in kilobits.

Calculate the time taken.

14. A 352 MB file at 14 000.

Downloading music and videos Random selection

H. An MP3 player has 45 songs and three songs are played at random, without repeats. a How many different combinations are possible? b What is the probability that a particular song is played in the first three songs? a Number of combinations

= 45× 44× 43= 85,140

b Probability

= 345

= 115

15. Complete the following to find: a the number of ways three songs can be chosen from 36 without repeats Number of songs = ____ × 35 × ____ = _____ b the probability that a particular song is played in the first three songs

Probability = = 1

12

16. a Find the number of ways three songs can be chosen from 50 without repeats.

b What is the probability that a particular song is played in the first three songs?

This was seen in the Probability topic earlier in the year.

There are three opportunities for the song to be played out of the 45 combinations.

Illegal Downloads

7000 people were surveyed on the types of illegal downloads they obtained, as well as how much they would pay for a legal equivalent. The results are shown in the graphs below.

How much would you pay for a legal equivalent?

17. What percentage of people surveyed illegally downloaded movies?

18. How many people is this?

19. What percentage of people would pay nothing for television downloads?

20. How many people who downloaded music were prepared to pay for it?

0%  

10%  

20%  

30%  

40%  

50%  

60%  

70%  

80%  

90%  

100%  

Music   Movies   Television  

Types  of  illegal  downloads  

Nothing 21.6%

$2 45.6%

$5 28.3%

$10 4.4%

Movies  

Nothing 33.6%

50c 48.9%

$1 14.7%

$2 2.8%

Music  

Nothing 33.6%

$1 39.3%

$2 18.7%

$3 8.4%

Television  

Review

The image above shows the capacity of a backup hard drive. Answer the following questions.

21. What percentage is the Used Space of the Total?

22. The total space is 7.21 TB, what is this capacity in gigabytes?

23. A photographer is using this backup drive for high resolution photos. Each photo is approximately 18.2 MB. How many photos could this drive store?

This image shows a download in progress.

24. How long in seconds would it have taken to download the entire file is the download speed remained constant?