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You want to map every possible image of size 64 x 64 to a binary category (cat or non-cat). Each image has 3 channels and each pixel in each channel can take an integer value between (and including) 0 and 255. Source: http://cs230.stanford.edu/files/cs230exam_win18.pdf

I would have assumed that each pixel value takes 8 bit times 64^2 pixels for each image times 3 for each channel PLUS 1 for the respective category in total: 8*64^2*3+1.

However, the correct solution is 256^{3×64×64}. What am I missing? Thanks in advance.

canadair
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2 Answers2

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I think most people missed the first line of the question:

"You want to map every possible image of size 64 x 64 to a binary category (cat or non-cat)"

If the question asked how many bits are needed to map one image, then your answer is correct: 256 * 64 * 64 * 3

However, the question asked the amount bits needed to map all possible combinations, so the correct answer should be: 256 ^ (64 * 64 * 3)

xuguo
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With 64x64 image and 3 channel you have 64x64x3 total units that you need to fill.
For first unit you can fill it with 256 values (0 to 255)
For second unit you can fill it with 256 values
So you can fill first two units in 256x256=256^2 ways since you can choose any combination of the integers. Similarly you can fill first three units in 256x56x256=256^3 ways.
Thus you can fill all the units i.e., the entire image in 256^(64x64x3) ways since you have 256 option to choose from for each of 64x64x3 units.

xashru
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