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Data Representation and Multimedia: Question 4

Syllabus 1.1, 1.2, 1.3

Structured AS 8 marks

A photo-editing app is used to create a poster. A bitmap image in the app has a resolution of 800 x 600 pixels and a colour depth of 24 bits per pixel (true colour).

(a) Calculate the uncompressed file size of this bitmap image in bytes. Show your working. [3]

(b) Convert your answer to part (a) into kibibytes (KiB), where 1 KiB = 1024 bytes. [2]

(c) The designer needs to enlarge this image to a much bigger poster size without losing quality, and is deciding whether to keep it as a bitmap or redraw it as a vector graphic. State which format is more suitable for this purpose, and explain your answer with reference to how each format stores image data. [3]

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Worked solution

Part (a): Uncompressed file size in bytes

Total number of pixels:

800 x 600 = 480,000 pixels

Bits per pixel = colour depth = 24 bits. Total number of bits:

480,000 x 24 = 11,520,000 bits

File size is normally given in bytes, and 1 byte = 8 bits, so:

11,520,000 / 8 = 1,440,000 bytes

[3 marks]: [1] for the total pixel count (480,000), [1] for multiplying by the colour depth to get the total in bits (11,520,000 bits), [1] for correctly converting bits to bytes (1,440,000 bytes).

Part (b): Converting to kibibytes

1 KiB = 1024 bytes, so:

1,440,000 / 1024 = 1406.25 KiB

(Check: 1024 x 1406 = 1,439,744, and 1,440,000 - 1,439,744 = 256, and 256 / 1024 = 0.25, confirming 1406.25 KiB exactly.)

[2 marks]: [1] for dividing by 1024 (the binary prefix), not 1000, [1] for the correct value 1406.25 KiB.

Part (c): Bitmap vs vector graphic for enlarging

A vector graphic is the more suitable format for this poster.

A bitmap image stores a fixed grid of individual pixel values (its resolution is fixed at 800 x 600 for this image. Enlarging a bitmap means stretching this fixed number of pixels over a much larger area, so each pixel becomes visibly bigger, and the image becomes blocky and pixelated, losing sharpness) no new detail can be created.

A vector graphic instead stores a mathematical description of drawing objects (such as lines, curves and shapes) and their properties (position, size, colour, and so on), rather than individual pixels. When the image is enlarged, the software simply recalculates and redraws these objects at the new size, so edges stay sharp and there is no pixelation, whatever size the poster is printed at.

[3 marks]: [1] for correctly identifying vector graphic as the more suitable format, [1] for describing how a bitmap’s fixed pixel grid causes pixelation/loss of quality when enlarged, [1] for describing how a vector graphic’s drawing objects/properties can be redrawn at any size without loss of quality.

Final answers

  • (a) 1,440,000 bytes
  • (b) 1406.25 KiB
  • (c) Vector graphic, it stores scalable drawing objects/properties rather than a fixed pixel grid