Question

Рисунок размером 1024х512 пикселей сохранили в виде несжатого файла размером 1,5 Мб. Какое количество информации было использовано для кодирования цвета пикселя? Каково максимально возможное число цветов в палитре, соответствующей такой глубине цвета?

Answer 1

Точек в изображении:1024×512=2¹°×2⁹=2¹⁹; размер файла:
1,5Мб=1,5×1024×1024×8=12×2²°бит; 
 одна точка кодируется  12×2²°:2¹⁹= 24 битами, в палитре будет 2²⁴=16777216 цветов

Answer 2

Calculating Information Used for Pixel Color Encoding and Maximum Possible Colors

To calculate the amount of information used for encoding the color of a pixel and the maximum possible number of colors in the palette, we can use the following information:

- The image size is 1024x512 pixels. - The file size is 1.5 MB.

The formula to calculate the amount of information used for encoding the color of a pixel is:

N = 2^i

Where: - N = number of colors - i = number of bits used to represent each pixel

The maximum possible number of colors in the palette, corresponding to such a color depth, can be calculated using the formula:

N = 2^i

Let's calculate the amount of information used for encoding the color of a pixel and the maximum possible number of colors in the palette.

Calculations

1. Amount of Information Used for Encoding Color of a Pixel: - The image size is 1024x512 pixels. - The file size is 1.5 MB. - Using the given information, we can calculate the amount of information used for encoding the color of a pixel.

According to the provided source the calculation for the amount of information used for encoding the color of a pixel is as follows: - 64 * 512 = 32768 - 32768 / 32768 = 1 (bit)

Therefore, the amount of information used for encoding the color of a pixel is 1 bit.

2. Maximum Possible Number of Colors in the Palette: - Using the same formula, we can calculate the maximum possible number of colors in the palette.

According to the provided source the calculation for the maximum possible number of colors in the palette is as follows: - N = 2^i - i = 8 - N = 256

Therefore, the maximum possible number of colors in the palette, corresponding to such a color depth, is 256.

Conclusion

The amount of information used for encoding the color of a pixel is 1 bit, and the maximum possible number of colors in the palette, corresponding to such a color depth, is 256.