If the frame buffer has 10-bits per pixel and 8-bits are allocated for each of…
2018
If the frame buffer has 10-bits per pixel and 8-bits are allocated for each of the \(𝑅,𝐺\), and \(𝐵\) components, then what would be the size of the color lookup table (LUT)?
- A.
\((2^8+2^9)\)bytes - B.
\((2^{10}+2^8)\)bytes - C.
\((2^{10}+2^{24})\)bytes - D.
\((2^{10}+2^{11})\)bytes
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Correct answer: D
Answer: The color lookup table size is 3072 bytes.
Number of LUT entries = number of distinct frame-buffer values = 2^10 = 1024 entries.
Storage per LUT entry = 8 bits for R + 8 bits for G + 8 bits for B = 24 bits = 3 bytes.
Total LUT size = 1024 entries × 3 bytes per entry = 3072 bytes.
Note: The expression (2^10 + 2^11) equals 1024 + 2048 = 3072, which is another way to represent 3 × 2^10 bytes. A common mistake is to confuse the pixel bit depth per component with the frame-buffer index width; here the frame buffer index width (10 bits) determines the number of LUT entries, while 8 bits per component determine the storage per entry.