Calculate bitmap image file sizes based on the number of pixels and colour…

The idea

A bitmap is a grid of pixels, and each pixel stores a binary code whose length equals the colour depth in bits. To find the file size, multiply the number of pixels by the colour depth: file size in bits = number of pixels × colour depth. For a 200 × 100 image at 4 bits per pixel, the pixel count is 200 × 100 = 20 000, so the size is 20 000 × 4 = 80 000 bits. Divide by 8 for bytes (10 000 bytes), then by 1000 for kilobytes (10 kB) or by 1024 if the question uses kibibyte-style units. Always state the unit and check whether the question wants bits, bytes or kB.

What earns the marks

• Identify the number of pixels, multiplying width by height when the image dimensions are given rather than the pixel total.
• Identify the colour depth as the number of bits stored per pixel.
• Multiply number of pixels by colour depth to obtain the file size in bits.
• Convert bits to bytes by dividing by 8, and to kB by dividing by 1000 (or by 1024 where the question specifies that convention).
• State the final answer with a correct unit and show the working so the method is visible.

Common mistakes and how to put them right

• Multiplying width by colour depth only and ignoring height.

  Put it right: Multiply width × height first to get the total pixel count.

• Confusing colour depth with the number of colours.

  Put it right: Use the bit value, since 8 colours means a colour depth of 3 bits.

• Reporting the answer in bits when bytes were requested.

  Put it right: Divide the bit total by 8 and label the unit.

Exam tips

• Write the formula down first (pixels × colour depth) so each substitution is clear.
• Convert units at the end and check the question's requested unit before finalising.
• Sanity-check magnitude: a small image at low colour depth should give a small file size.