Given an image of size 1024 × 1024 pixels in which intensity of each pixel is…
2014
Given an image of size 1024 × 1024 pixels in which intensity of each pixel is an 8-bit quality. It requires _______ of storage space if the image is not compressed.
- A.
one Terabyte
- B.
one Megabyte
- C.
8 Megabytes
- D.
8 Terabytes
Attempted by 180 students.
Show answer & explanation
Correct answer: B
Answer: one Megabyte
Reasoning: Step-by-step calculation
Number of pixels = 1024 × 1024 = 1,048,576 pixels.
Bits required = pixels × bits per pixel = 1,048,576 × 8 = 8,388,608 bits.
Convert bits to bytes: 8,388,608 ÷ 8 = 1,048,576 bytes.
Convert bytes to megabytes: 1,048,576 bytes = 1 megabyte (1 MB = 2^20 bytes).
Why the other choices are incorrect:
one Terabyte is far too large; a terabyte is on the order of 10^12 bytes, while the image needs only 1,048,576 bytes.
8 Megabytes overestimates the requirement by a factor of eight. 8 MB = 8 × 1,048,576 = 8,388,608 bytes, not the 1,048,576 bytes computed.
8 Terabytes is many orders of magnitude larger than needed and is not realistic for this calculation.