Data Storage & Compression

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Lesson notes

Units of Data Storage

A bit (b) is the smallest unit, representing a 1 or 0.
A nibble = 4 bits; a byte (B) = 8 bits.
Larger units: Kibibyte (KiB) = 1024 B, Mebibyte (MiB) = 1024 KiB, Gibibyte (GiB) = 1024 MiB, Tebibyte (TiB) = 1024 GiB, Pebibyte (PiB) = 1024 TiB, Exbibyte (EiB) = 1024 PiB.
Binary prefixes (KiB, MiB) use powers of 2 (1024); decimal prefixes (KB, MB) use powers of 10 (1000).
To convert to a larger unit, divide by 1024; to a smaller unit, multiply by 1024.
Between bits and bytes: multiply/divide by 8.

Calculating File Sizes

Bitmap image size = Resolution × Colour Depth (or width × height × colour depth).
Resolution = width × height in pixels; colour depth = bits per pixel.
Sound file size = Sample Rate × Duration (seconds) × Sample Resolution.
Sample rate = samples per second; sample resolution = bits per sample.
Convert bits to bytes by dividing by 8; bytes to KiB by dividing by 1024.

Compression Overview

Compression reduces file size to save storage space, reduce bandwidth, and shorten transmission time.
Two types: lossy and lossless.

Lossy Compression

Lossy compression permanently removes data to reduce file size; it is irreversible.
Achieves large size reductions but at the cost of quality loss.
Suitable for images, video, and sound where some quality loss is acceptable.
Example: grouping similar colours in a photograph reduces colour count while keeping visual quality.

Lossless Compression

Lossless compression encodes data to reduce size without losing information; it is reversible.
Produces smaller files than original but not as small as lossy.
Suitable for text/documents where quality must be preserved.
Uses algorithms like Run-Length Encoding (RLE) to find patterns and repetition.

Run-Length Encoding (RLE)

RLE compresses consecutive identical elements into a count and the value.
Example: `AAAABBBCCDAA` becomes `4A3B2C1D2A`.
Used in bitmap images to compress runs of the same colour (e.g., `5R3B` for 5 red, 3 blue pixels).

Slides

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Practice questions

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1.Which of the following is the smallest unit of data storage?
Easy
- ABit
- BByte
- CNibble
- DKilobyte
2.How many bits are there in one byte?
Easy
- A4
- B8
- C16
- D1024
3.What is the value of 1 KiB (kibibyte) in bytes?
Easy
- A1000
- B1024
- C8
- D1024²
4.Convert 2 MiB to KiB.
Easy
- A2048
- B2000
- C1024
- D4096
5.A sound file has a sample rate of 44,100 Hz, a duration of 10 seconds, and a sample resolution of 16 bits. What is the file size in bytes?
Medium
- A882,000
- B705,600
- C7,056,000
- D44,100
6.Which formula correctly calculates the size of a bitmap image?
Easy
- AResolution × colour depth
- BWidth × height × sample rate
- CSample rate × duration × colour depth
- DWidth × height × duration
7.What is compression?
Easy
- AReducing the size of a file
- BIncreasing the quality of a file
- CConverting a file to a different format
- DEncrypting a file for security
8.Which type of compression is irreversible?
Easy
- ALossy
- BLossless
- CRun length encoding
- DAll compression

More questions

9.Run length encoding (RLE) is an example of which type of compression?
Easy
- ALossy
- BLossless
- CBoth lossy and lossless
- DNeither
10.What is the RLE compression of the string 'WWWWBBWWW'?
Medium
- A4W2B3W
- BW4B2W3
- C4W2B2W
- D3W2B4W
11.A bitmap image has a width of 800 pixels, height of 600 pixels, and a colour depth of 8 bits. What is its size in KiB?
Medium
- A468.75
- B3750
- C480000
- D58.59
12.Which of the following is a benefit of using lossy compression for a sound file sent via email?
Easy
- AThe file size is reduced, making it quicker to transmit
- BThe file can be restored to its original state
- CNo data is lost during compression
- DThe sound quality is improved
13.A bitmap image has a resolution of 1920 × 1080 pixels and a colour depth of 16 bits. What is its size in mebibytes (MiB)?
Medium
- A3.95 MiB
- B31.6 MiB
- C7.9 MiB
- D1.98 MiB
14.A sound file is recorded with a sample rate of 44.1 kHz, a sample resolution of 16 bits, and a duration of 2 minutes. What is the file size in mebibytes?
Hard
- A10.1 MiB
- B80.6 MiB
- C5.05 MiB
- D1.26 MiB
15.An uncompressed bitmap image has a size of 2 MiB. It has a colour depth of 8 bits. What is its approximate resolution (total number of pixels)?
Medium
- A2,097,152 pixels
- B262,144 pixels
- C16,777,216 pixels
- D524,288 pixels
16.Which of the following is a lossless compression technique?
Easy
- ARun-length encoding (RLE)
- BRemoving similar colours from an image
- CReducing the sample rate of a sound file
- DDecreasing the colour depth of an image
17.A line of a bitmap image contains the following pixel colours: RRRRGGGBBB. Using run-length encoding (RLE), how would this line be represented?
Medium
- A4R3G3B
- B3R3G3B
- C4R3G2B
- D3R4G3B
18.A text file uses lossless compression. The original file size is 100 KiB. After compression, the file size is 40 KiB. What is the compression ratio?
Medium
- A2.5:1
- B0.4:1
- C5:2
- D100:40
19.A student compresses a photograph using lossy compression. Which of the following is a likely consequence?
Easy
- AThe file size is reduced but some image quality is lost.
- BThe file size is reduced and the image quality is unchanged.
- CThe file size increases to preserve image quality.
- DThe file can be decompressed to its exact original state.
20.An image has a colour depth of 24 bits. How many different colours can be represented per pixel?
Easy
- A16,777,216
- B256
- C65,536
- D16,384
21.A sound file has a size of 5 MiB. It is recorded with a sample resolution of 16 bits and a sample rate of 22,050 Hz. What is the approximate duration of the sound in seconds?
Hard
- A119 seconds
- B238 seconds
- C59.5 seconds
- D476 seconds
22.How many bits are there in 3 bytes?
Easy
- A24
- B12
- C8
- D32
23.Which of the following is the largest unit of data storage?
Easy
- AExbibyte (EiB)
- BGibibyte (GiB)
- CPebibyte (PiB)
- DTebibyte (TiB)
24.A student measures the size of a file as 2.5 KiB. How many bytes is this?
Easy
- A2500
- B2560
- C2048
- D2000
25.A bitmap image has a resolution of 1920 × 1080 pixels and a colour depth of 24 bits. What is its size in mebibytes (MiB)?
Medium
- A5.93
- B4.75
- C6.91
- D7.10
26.Which of the following is an example of lossy compression?
Easy
- ARun-length encoding (RLE)
- BJPEG
- CZIP
- DPNG
27.What is the main advantage of lossless compression over lossy compression?
Easy
- AIt produces smaller file sizes
- BIt is faster to compress
- CIt allows the original data to be perfectly reconstructed
- DIt is suitable for all types of data
28.How many different colours can be represented per pixel with a colour depth of 24 bits?
Easy
- A24
- B256
- C16,777,216
- D16,384
29.How many bits are there in a nibble?
Easy
- A4
- B8
- C2
- D16
30.What is the value of 1 mebibyte (MiB) in kibibytes (KiB)?
Easy
- A1024 KiB
- B1000 KiB
- C1024 B
- D1000 B
31.Which of the following is the correct order of units from smallest to largest?
Easy
- Abit, byte, nibble, kibibyte
- Bbit, nibble, byte, kibibyte
- Cnibble, bit, byte, kibibyte
- Dbyte, bit, nibble, kibibyte
32.A file is 3 KiB in size. How many bytes is this?
Easy
- A3072 bytes
- B3000 bytes
- C3072 bits
- D3000 bits
33.How many bytes are there in 2 GiB?
Medium
- A2,147,483,648 bytes
- B2,000,000,000 bytes
- C2,097,152 bytes
- D2,048 bytes
34.What is the main disadvantage of lossy compression compared to lossless compression?
Easy
- AData is permanently lost and cannot be restored
- BIt always produces larger files
- CIt is slower to transmit
- DIt cannot be used for images
35.Which of the following is a benefit of using lossy compression for a photograph sent via email?
Easy
- ASmaller file size so faster to send
- BThe original quality is preserved exactly
- CThe file can be decompressed to its original state
- DIt uses less processing power to compress
36.A student records a sound using a sample rate of 44.1 kHz and a sample resolution of 16 bits. The recording is 30 seconds long. What is the file size in kibibytes?
Hard
- A2584 KiB
- B20672 KiB
- C258 KiB
37.A student measures the size of an uncompressed bitmap image. The image has a resolution of 800 × 600 pixels and a colour depth of 16 bits. What is the file size in kibibytes (KiB)?
Medium
- A937.5 KiB
- B468.75 KiB
- C7,680,000 KiB
- D960 KiB
38.A sound file is recorded with a sample rate of 22,050 Hz, a sample resolution of 8 bits, and a duration of 30 seconds. What is the file size in kibibytes?
Medium
- A516.6 KiB
- B646.0 KiB
- C5,292,000 KiB
- D258.3 KiB
39.A bitmap image has a width of 1024 pixels and a height of 768 pixels. It is stored with a colour depth of 24 bits. The image is compressed using lossless compression, reducing its size by 40%. What is the size of the compressed image in mebibytes (MiB)?
Hard
- A1.35 MiB
- B2.25 MiB
- C0.9 MiB
- D3.0 MiB
40.A line of a bitmap image contains the following pixel colours: RRRRGGGBB. Using run-length encoding (RLE), how would this line be represented?
Medium
- A4R3G2B
- BR4G3B2
- C3R4G2B
- D4R3G1B
41.Match each unit of data storage to its correct symbol.
Easy
- Bit
- Byte
- Kibibyte
- Mebibyte
- b
- B
- KiB
- MiB
42.Arrange these units of data storage in order from smallest to largest: Byte, Pebibyte, Bit, Mebibyte.
Easy
- Bit
- Byte
- Mebibyte
- Pebibyte
43.Which of the following statements about lossy compression are correct? (Select all that apply)
Medium
- AIt is irreversible.
- BIt is suitable for text documents.
- CIt can greatly reduce file size.
- DIt groups similar colours together in images.
- EIt is also called run-length encoding.
44.Run-length encoding (RLE) is a lossless compression method.
Easy
True or false?
45.A bitmap image has a size of 3 MiB. It has a colour depth of 24 bits. What is the approximate number of pixels in the image?
Hard
- A1,048,576 pixels
- B1,024,000 pixels
- C3,145,728 pixels
- D262,144 pixels
46.Which of the following are benefits of using lossy compression for a photograph? (Select all that apply)
Medium
- AThe file size is reduced
- BThe original quality can be restored exactly
- CIt takes less time to upload the photograph to a website
- DThe photograph can be stored in less space on a memory card
47.A student compresses a text file using run-length encoding (RLE). The original string is 'AABBBCCCC'. What is the compressed representation?
Easy
- A2A3B4C
- BA2B3C4
- C2A3B4C1D
- D3A2B4C
48.Lossy compression is reversible.
Easy
True or false?
49.Which of the following are benefits of using lossless compression for a document? (Select all that apply)
Medium
- AThe original data can be recovered exactly
- BFile size is reduced more than with lossy compression
- CThe document takes up less storage space
- DThe document can be transmitted more quickly
- EThe quality of images in the document is permanently reduced
50.Match each compression type to its correct characteristic.
Easy
- Lossy compression
- Lossless compression
- Irreversible
- Reversible
- Used for text files
- Reduces quality permanently
51.Complete the RLE compressed representation: The string 'WWWWBBWWW' is compressed to ___.
Easy
The string 'WWWWBBWWW' is compressed to ____.
52.A bitmap image has a resolution of 1920 × 1080 pixels and a colour depth of 24 bits. What is its file size in mebibytes (MiB)? Give your answer to two decimal places.
Medium
53.A sound file is recorded with a sample rate of 44,100 Hz, a sample resolution of 16 bits, and a duration of 2 minutes. What is its file size in mebibytes (MiB)? Give your answer to two decimal places.
Medium
54.Complete the sentence.
Easy
Lossy compression is ____ because the original data cannot be recovered.
55.Use run-length encoding (RLE) to compress the following string. Write the compressed representation in the blank.
Easy
String: WWWWBBWWW Compressed: ____
56.State the formula used to calculate the size of a bitmap image file.
Easy
57.A bitmap image has a resolution of 1920 × 1080 pixels and a colour depth of 16 bits. What is its size in mebibytes (MiB)? Give your answer to two decimal places.
Medium
58.Complete the RLE compressed representation.
Easy
The string 'WWWWBBWWW' is compressed to ____.
59.A sound file is recorded with a sample rate of 44,100 Hz, a sample resolution of 16 bits, and a duration of 30 seconds. What is its size in kibibytes (KiB)?
Medium
60.A sound file is recorded with a sample rate of 44,100 Hz, a sample resolution of 16 bits, and a duration of 30 seconds. What is its size in kibibytes (KiB)? Give your answer to the nearest whole number.
Medium
61.A bitmap image has a width of 800 pixels and a height of 600 pixels. It has a colour depth of 8 bits. What is its file size in kibibytes (KiB)?
Medium
62.State the formula for calculating the size of a sound file.
Easy
63.Explain two reasons why using lossy compression for a sound file sent via email is beneficial.
Medium
64.Explain how run-length encoding (RLE) compresses data in a bitmap image.
Medium
65.A bitmap image has a resolution of 1920 × 1080 pixels and a colour depth of 24 bits. What is its file size in mebibytes (MiB)? Give your answer to two decimal places.
Medium
- A5.93 MiB
- B7.93 MiB
- C4.93 MiB
- D6.93 MiB
66.A sound file is recorded with a sample rate of 44,100 Hz, a sample resolution of 16 bits, and a duration of 2 minutes. What is its file size in mebibytes (MiB)? Give your answer to two decimal places.
Medium
- A12.09 MiB
- B10.09 MiB
- C11.09 MiB
- D9.09 MiB
67.A bitmap image has a resolution of 1920 × 1080 pixels and a colour depth of 16 bits. What is its size in mebibytes (MiB)? Give your answer to two decimal places.
Medium
- A2.96 MiB
- B3.96 MiB
- C4.96 MiB
- D5.96 MiB
68.A sound file is recorded with a sample rate of 44,100 Hz, a sample resolution of 16 bits, and a duration of 30 seconds. What is its size in kibibytes (KiB)?
Medium
- A2842.38 KiB
- B2325.58 KiB
- C3100.78 KiB
- D2583.98 KiB
69.A bitmap image has a width of 800 pixels and a height of 600 pixels. It has a colour depth of 8 bits. What is its file size in kibibytes (KiB)?
Medium
- A515.63 KiB
- B562.51 KiB
- C421.87 KiB
- D468.75 KiB

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