Question

Несжатое растовое изображение размером 256*128 пикселей занимает 16 КБайт памяти, какого мах возможное число цветов в палитере изображения?

Answer 1

I = K * i (I - объем информации, K - кол-во пикселей, i - вес одного пикселя / глубина цвета)

i = I / K

K = 128 * 256 = 32768 пикселей

I = 16 Kb = 16 * 1024 * 8 бит = 131072 бит

Глубина цвета $i = \frac{I}{K} = \frac{131072}{32768} = 4.0 ~= 4$ бит (округляем в меньшую сторону так, как тут могут быть только целые числа)

Кол-во цветов в палитре $N = 2^i = 2^{4} = 16$ цветов

Ответ: 16

Answer 2

Number of Colors in an Uncompressed Image

An uncompressed raster image with a size of 256x128 pixels and occupying 16 KB of memory can have a maximum number of colors determined by the color depth of the image. The color depth refers to the number of bits used to represent each pixel in the image.

To calculate the maximum number of colors, we need to determine the color depth of the image. The color depth can be calculated using the formula:

Color Depth = Total Number of Bits / Number of Pixels

In this case, the image occupies 16 KB of memory, which is equivalent to 16,384 bytes (16 KB * 1024 bytes/KB). Since each byte consists of 8 bits, the total number of bits in the image is 16,384 * 8 = 131,072 bits.

The image has a size of 256x128 pixels, which means it contains a total of 256 * 128 = 32,768 pixels.

Using the formula mentioned earlier, we can calculate the color depth:

Color Depth = 131,072 bits / 32,768 pixels = 4 bits per pixel

Therefore, the maximum number of colors in the palette of the image is determined by the number of possible combinations of 4 bits, which is 2^4 = 16 colors.

Thus, the maximum possible number of colors in the palette of the uncompressed image is 16 colors.

Please note that this calculation assumes that the image uses a fixed palette with a limited number of colors. If the image uses a different color model or allows for variable colors, the number of possible colors may be different.