Representing images: Size = (bits) = W x H x D

The idea

An image is stored as a grid of pixels, and each pixel carries a colour code. W is the image width in pixels, H is the height in pixels, and D is the colour depth in bits per pixel. Multiplying W × H gives the total number of pixels; multiplying again by D gives the total number of bits needed, because every pixel needs D bits. Example: a 4 × 3 pixel image at depth 2 bits has 4 × 3 × 2 = 24 bits. Keep the units as bits throughout; do not divide by 8 here, since dividing converts to bytes. If a question asks for bits, stop at this result. Check that W, H and D are all in the stated units before multiplying, and remember that a larger colour depth means more bits per pixel and therefore a larger file.

What earns the marks

• Identify W as width in pixels, H as height in pixels and D as colour depth in bits per pixel.
• Multiply W × H to obtain the total number of pixels in the image.
• Multiply the pixel count by D to obtain the total number of bits.
• State the answer in bits and do not divide by 8 when bits are requested.
• Worked example: 4 × 3 × 2 = 24 bits for a 4 by 3 image at 2-bit depth.

Common mistakes and how to put them right

• Dividing by 8 when the question asks for bits.

  Put it right: The division converts bits to bytes, so it should only be done when bytes are required.

• Treating D as the number of colours rather than bits per pixel.

  Put it right: D is the colour depth in bits, so use the bit value directly.

• Multiplying only W × H and forgetting D.

  Put it right: That gives pixels, not bits, so the depth factor must be included.

Exam tips

• Write the formula W × H × D first, then substitute the numbers so units stay clear.
• Check whether the question asks for bits or bytes before deciding whether to divide by 8.
• Sanity-check the magnitude: more pixels or greater depth must give a larger bit total.