Question

A square digital image of size 128 × 128 pixels requires 65536 bits of storage. What is the number of grey levels?

• A. 16
• B. 4
• C. 8
• D. 32

Hint:

Find bits per pixel by dividing total storage bits by the total number of pixels, then use grey levels = 2^(bits per pixel).

Answer 1

The Correct Option is A

Step 1: Set up the storage relation.
An image of size \(M \times N\) pixels, with each pixel stored using \(k\) bits, needs a total storage of \(M \times N \times k\) bits. Here \(M = N = 128\), so the total number of pixels is \(128 \times 128 = 16384\).

Step 2: Find the bits per pixel.
The image needs 65536 bits in total, so the number of bits allotted to each pixel is \[ k = \frac{65536}{16384} = 4 \text{ bits/pixel} \]

Step 3: Convert bits per pixel to grey levels.
If a pixel is stored using \(k\) bits, the number of distinct grey levels it can represent is \(L = 2^k\). With \(k = 4\), \[ L = 2^4 = 16 \]

Step 4: Eliminate the wrong options.
Option (B) 4 would need only \(k=2\) bits/pixel, giving \(128\times128\times2 = 32768\) bits, not 65536. Option (C) 8 needs \(k=3\), giving \(49152\) bits. Option (D) 32 needs \(k=5\), giving \(81920\) bits. None match the given 65536 bits, so 16 grey levels is the only value consistent with the data. \[ \boxed{L = 16} \]