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

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1 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 The abbreviation for byte is B. Bits vs Bytes as Fast As Possible 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 = 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!! 7200 b = = 900 B the size. Therefore, divide. 3. Convert 1200 bits to bytes b = 8 = B 4. Convert 984 bits to bytes.

2 Units of storage These units of storage are given in the HSC Examination Formulae and Data Sheet. Unit Relationship DATA SHEET 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 B kb MB GB TB 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 = kb = 8192 kb 5. Convert 4 GB to MB. 6. Convert 7168 kb to bytes. 4 GB = 1024 MB = MB 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 kb = MB = 3 MB 7. Convert 4608 GB to TB. 8. Convert 7168 kb to bytes GB = TB = 4.5 TB

3 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 = 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 Therefore, divide. Number of songs = = 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 Think, why should you round the calculated answer down? 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

4 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 = bytes = bytes Then convert to bits. = bits = bits Then convert to kilobits. = kilobits = kilobits Convert the time to seconds. 50 mins 25 seconds = seconds = 3025 seconds Download speed = Data Time = 3025 = = 882 kbps This is the amount of data. This is the time taken in seconds. 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 = Data Time = = kbps kbps 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.

5 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 = bytes = bytes Then convert to bits. = bits = bits Then convert to kilobits. = kilobits Time = Data Speed = kilobits = 37, = s This is the amount of data. The speed was given in the question. 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 Convert to bytes. = 8,388,608 bytes = 8,388,608 bits = 67,108,864 bits = 67,108,864 kilobits = kilobits Time = Data Speed = 100 = Convert to bits. Convert to kilobits. Calculate the amount of data in kilobits. Calculate the time taken.

6 14. A 352 MB file at 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 = = 85,140 b Probability = 3 45 = 1 15 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. 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 = = 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?

7 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. Types of illegal downloads 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Music Movies Television How much would you pay for a legal equivalent? $10 4.4% Movies Music $2 2.8% Television $3 8.4% $5 28.3% Nothing 21.6% $1 14.7% Nothing 33.6% $2 18.7% Nothing 33.6% $2 45.6% 50c 48.9% $1 39.3% 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?

8 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?