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Representing Text, Sound, Images and Storage: Question 7

Syllabus 1.2

Multiple choice 1 mark

A digital art app lets the user choose from a palette of exactly 16 different colours for each pixel of an image.

What is the minimum colour depth, in bits, needed to represent 16 different colours per pixel?

Choose an answer to check it, then compare with the worked solution below.
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Worked solution

Why the other options are wrong

  • (A) is incorrect: 2 bits can only produce 2^2 = 4 different colours, which is not enough to give each of the 16 colours its own unique code.
  • (C) is incorrect: 8 bits would allow 2^8 = 256 different colours, which is far more than the minimum needed for a 16-colour palette.
  • (D) is incorrect: this wrongly assumes the colour depth must equal the number of colours (16), rather than finding the smallest number of bits that can produce at least 16 different codes.

Why B is correct

Colour depth is the number of bits used to store the colour of a single pixel, and n bits can produce 2^n different binary codes, so 2^n different colours can be represented. To find the minimum colour depth needed for 16 colours, check increasing values of n:

  • 2^3 = 8, not enough, since the palette has 16 colours.
  • 2^4 = 16, exactly enough to give each of the 16 colours its own unique code.

So the minimum colour depth needed is 4 bits.

Final answer

B. A colour depth of 4 bits gives exactly 2^4 = 16 different colour codes, matching the size of the palette.