Ravi draws a picture on a piece of paper measuring 5 inches × 4 inches. He…
2024
Ravi draws a picture on a piece of paper measuring 5 inches × 4 inches. He wants to scan the picture at 500 pixels per inch (ppi) in both horizontal and vertical directions and 16-bit colour. Without file compression, what is the approximate file size of the scanned image (in MB)?
Answer: D. 9.54 — ConceptFor an uncompressed raster image, total bits = width in pixels × height in pixels × colour depth. Scanner resolution in pixels per inch applies along…
- A.
7.82
- B.
6.33
- C.
8.66
- D.
9.54
Show answer & explanation
Correct answer: D
Concept
For an uncompressed raster image, total bits = width in pixels × height in pixels × colour depth. Scanner resolution in pixels per inch applies along each dimension. Also, 8 bits = 1 byte and 1 MiB = 1,048,576 bytes.
Application
The width is 5 × 500 = 2,500 pixels, and the height is 4 × 500 = 2,000 pixels.
The total number of pixels is 2,500 × 2,000 = 5,000,000.
The uncompressed size is 5,000,000 × 16 = 80,000,000 bits = 10,000,000 bytes.
Using the binary megabyte convention, 10,000,000 ÷ 1,048,576 ≈ 9.5367 MB, which rounds to 9.54 MB.
Cross-check
Using the area directly gives 5 × 4 × 500 × 500 × 16 ÷ 8 = 10,000,000 bytes, the same byte count.
Therefore, the approximate uncompressed file size is 9.54 MB.