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GCSE Computer Science · 1.2.3

Units of Data

Section A: 10 multiple choice questions, 10 marks. Section B: 5 written questions, 17 marks. Total 27 marks.

Name

Class

Date

Mark  / 27

Section A

Circle the letter of the correct answer. One mark each.

  1. 1How many bits are in a byte?1
    1. A4
    2. B8
    3. C16
    4. D1000
  2. 2According to the OCR specification, how many bytes are in a kilobyte?1
    1. A8
    2. B100
    3. C1000
    4. D1024
  3. 3An image is 200 by 100 pixels with a colour depth of 4 bits. What is its file size in bits?1
    1. A10,000
    2. B20,000
    3. C80,000
    4. D800,000
  4. 4Convert 24,000,000 bits into megabytes.1
    1. A24 MB
    2. B192 MB
    3. C0.3 MB
    4. D3 MB
  5. 5A colour depth of 8 bits allows how many different colours?1
    1. A8
    2. B64
    3. C256
    4. D1024
  6. 6Why do computers use binary rather than denary?1
    1. AElectronic components have two reliable states, on and off
    2. BBinary numbers are shorter than denary numbers
    3. CDenary was invented after computers
    4. DBinary uses less electricity per digit
  7. 7A 20 second sound clip is sampled at 8000 Hz with a bit depth of 8. What is the file size in bits?1
    1. A12,800
    2. B160,000
    3. C640,000
    4. D1,280,000
  8. 8What is a nibble?1
    1. A4 bits
    2. B16 bits
    3. C2 bits
    4. D8 bits
  9. 9Which is the largest of these?1
    1. A5000 megabytes
    2. B900 gigabytes
    3. C1,000,000 kilobytes
    4. D1 terabyte
  10. 10A text file contains 2000 characters stored in ASCII using 7 bits each. What is the size in bytes?1
    1. A875
    2. B1750
    3. C2000
    4. D14,000

Section B

Answer in the space provided. The number of marks tells you how many separate points to make.

  1. 1ExplainExplain why data is stored in binary in a computer system.2
  2. 2CalculateAn image is 800 pixels wide and 600 pixels high, with a colour depth of 16 bits. Calculate the file size of the image in megabytes. Show your working.4
  3. 3CalculateA sound file is recorded for 4 minutes at a sample rate of 44,100 Hz with a bit depth of 16 bits. Calculate the file size in megabytes, showing your working.4
  4. 4StateState the number of bits in a nibble and the number of bits in a byte.2
  5. 5CalculateA school stores 3000 photographs. Each photograph is 2000 by 1500 pixels with a colour depth of 24 bits. Calculate the total storage required in gigabytes.5

Mark scheme

Section A

1B2C3C4D5C6A7D8A9D10B

Section B

1 Explain why data is stored in binary in a computer system. 2

One mark for each of the following, to a maximum of 2.

  • Electronic components have two states, such as on and off or high and low voltage
  • These two states directly represent 1 and 0, and are reliable to distinguish

Model answer. Data is stored in binary because the electronic components inside a computer, such as transistors, have two reliable states: they are either conducting or not conducting, which corresponds to a high or low voltage. These two states map directly onto the digits 1 and 0, and because there are only two of them they can be distinguished reliably even if the voltage varies slightly, which would not be true if ten separate levels had to be recognised for denary.

2 An image is 800 pixels wide and 600 pixels high, with a colour depth of 16 bits. Calculate the file size of the image in megabytes. Show your working. 4

One mark for each of the following, to a maximum of 4.

  • Multiplies colour depth by width by height: 16 x 800 x 600
  • Obtains 7,680,000 bits
  • Divides by 8 to obtain 960,000 bytes
  • Divides by 1000 twice to obtain 0.96 MB

Model answer. File size in bits is colour depth multiplied by width multiplied by height, so 16 x 800 x 600 = 7,680,000 bits. Dividing by 8 converts this to 960,000 bytes. Dividing by 1000 gives 960 kilobytes, and dividing by 1000 again gives a final file size of 0.96 megabytes.

3 A sound file is recorded for 4 minutes at a sample rate of 44,100 Hz with a bit depth of 16 bits. Calculate the file size in megabytes, showing your working. 4

One mark for each of the following, to a maximum of 4.

  • Converts 4 minutes to 240 seconds
  • Multiplies sample rate by duration by bit depth
  • Obtains 169,344,000 bits
  • Converts to approximately 21.17 MB

Model answer. First convert the duration: 4 minutes is 4 x 60 = 240 seconds. File size in bits is sample rate x duration x bit depth, so 44,100 x 240 x 16 = 169,344,000 bits. Dividing by 8 gives 21,168,000 bytes, dividing by 1000 gives 21,168 kilobytes, and dividing by 1000 again gives a file size of approximately 21.17 megabytes.

4 State the number of bits in a nibble and the number of bits in a byte. 2

One mark for each of the following, to a maximum of 2.

  • A nibble is 4 bits
  • A byte is 8 bits

Model answer. A nibble contains 4 bits and a byte contains 8 bits, so a nibble is exactly half a byte.

5 A school stores 3000 photographs. Each photograph is 2000 by 1500 pixels with a colour depth of 24 bits. Calculate the total storage required in gigabytes. 5

One mark for each of the following, to a maximum of 5.

  • Calculates bits per image as 24 x 2000 x 1500
  • Obtains 72,000,000 bits per image
  • Converts to 9,000,000 bytes or 9 MB per image
  • Multiplies by 3000 photographs
  • Obtains 27,000 MB which is 27 GB

Model answer. For one photograph the file size in bits is 24 x 2000 x 1500 = 72,000,000 bits. Dividing by 8 gives 9,000,000 bytes, which is 9000 kilobytes or 9 megabytes per photograph. Multiplying by 3000 photographs gives 27,000 megabytes in total, and dividing by 1000 converts this to 27 gigabytes of storage required.