Question

Задача 2. Для хранения растрового изображения размером 32х32 пикселя отвели 512 байтов памяти. Каково максимально возможное число цветов в палитре изображения?1) 82) 23) 164) 236Задача 3. Для хранения растрового изображения размером 64х32 пикселя отвели 1 килобайт памяти. Каково максимально возможное число цветов в палитре изображения?1) 162) 323) 644) 1024Задача 4. Цвет пикселя монитора определяется тремя составляющими: зеленой, синей и красной. Под красную и синюю составляющие одного пикселя отвели по пять бит. Сколько бит отвели под зеленую составляющую одного пикселя, если растровое изображение размером8х8 пикселей занимает 128 байт памяти?1) 52) 63) 84) 16Задача 5. Для хранения растрового изображения размером 32х64 пикселя отвели 512 байт памяти. Каково максимально возможное число цветов в палитре изображения?1) 20482) 10243) 164) Задача 6. Для хранения растрового изображения размером 128x128 пикселей отвели 4 килобайта памяти. Каково максимально возможное число цветов в палитре изображения?1) 82) 23) 164) 4

Answer 1

2)
32*32=2^10
512 байт =512*8 бит =2^9 *2^3=2^12
2^12 : 2^10 = 2^2 =4 бита для одного пикселя
2^4 =16 цветов ;  ответ 16 цветов.
3)
64*32 =2^11
1 Кбайт =2^10 байта =2^13 битов
2^13 : 2^11 =2^2=4 битов
2^4 =16 цветов   ответ 16
4) 
5+5 =10 битов под кр и син
8*8=2^6
128 байт=2^7 байт=2^10 бит
2^10 : 2^6 =2^4 =16 бит
16-10 =6 бит под зелёную  ответ 6 бит
5)
32*64=2^11
512 байт =2^9*2^3 бит =2^12 бит
2^12 : 2^11 = 2 бита под один пиксель
2^2 =4 цвета           ответ 4
6)
128 *128 = 2^14
4 Кбайта = 2^2 * 2^13 битов =2^15 битов
2^15 : 2^14 =2 бита под один пиксель
2^2=4 цвета   ответ 4

Answer 2

Task 2: Maximum number of colors in a palette for a 32x32 pixel image with 512 bytes of memory

To determine the maximum number of colors in a palette for a 32x32 pixel image with 512 bytes of memory, we need to calculate the number of bits available for each pixel and then determine the number of unique color combinations that can be represented.

Given that 512 bytes of memory are allocated for the image, and each pixel requires a certain number of bits to represent its color, we can calculate the number of bits available per pixel.

Since the image is 32x32 pixels, it contains a total of 32 * 32 = 1024 pixels.

To calculate the number of bits available per pixel, we divide the total number of bits available (512 bytes * 8 bits/byte) by the total number of pixels (1024 pixels):

512 bytes * 8 bits/byte / 1024 pixels = 4 bits/pixel

Therefore, each pixel can be represented using 4 bits.

To calculate the maximum number of colors in the palette, we raise 2 (the number of possible values for each bit) to the power of the number of bits per pixel:

2^4 = 16

Therefore, the maximum number of colors in the palette for a 32x32 pixel image with 512 bytes of memory is 16.

Task 3: Maximum number of colors in a palette for a 64x32 pixel image with 1 kilobyte of memory

To determine the maximum number of colors in a palette for a 64x32 pixel image with 1 kilobyte of memory, we follow a similar approach as in Task 2.

Given that 1 kilobyte of memory is allocated for the image, and each pixel requires a certain number of bits to represent its color, we can calculate the number of bits available per pixel.

Since the image is 64x32 pixels, it contains a total of 64 * 32 = 2048 pixels.

To calculate the number of bits available per pixel, we divide the total number of bits available (1 kilobyte * 8 bits/kilobyte) by the total number of pixels (2048 pixels):

1 kilobyte * 8 bits/kilobyte / 2048 pixels = 4 bits/pixel

Therefore, each pixel can be represented using 4 bits.

To calculate the maximum number of colors in the palette, we raise 2 (the number of possible values for each bit) to the power of the number of bits per pixel:

2^4 = 16

Therefore, the maximum number of colors in the palette for a 64x32 pixel image with 1 kilobyte of memory is 16.

Task 4: Number of bits allocated for the green component of a pixel in an 8x8 pixel image with 128 bytes of memory

To determine the number of bits allocated for the green component of a pixel in an 8x8 pixel image with 128 bytes of memory, we need to calculate the total number of bits used by the image and subtract the bits allocated for the red and blue components.

Given that the image is 8x8 pixels and occupies 128 bytes of memory, we can calculate the total number of bits used by the image:

128 bytes * 8 bits/byte = 1024 bits

Since the red and blue components of each pixel are allocated 5 bits each, the total number of bits allocated for the red and blue components is:

5 bits + 5 bits = 10 bits

To determine the number of bits allocated for the green component, we subtract the bits allocated for the red and blue components from the total number of bits used by the image:

1024 bits - 10 bits = 1014 bits

Therefore, the number of bits allocated for the green component of a pixel in an 8x8 pixel image with 128 bytes of memory is 1014 bits.

Task 5: Maximum number of colors in a palette for a 32x64 pixel image with 512 bytes of memory

To determine the maximum number of colors in a palette for a 32x64 pixel image with 512 bytes of memory, we follow a similar approach as in Task 2.

Given that 512 bytes of memory are allocated for the image, and each pixel requires a certain number of bits to represent its color, we can calculate the number of bits available per pixel.

Since the image is 32x64 pixels, it contains a total of 32 * 64 = 2048 pixels.

To calculate the number of bits available per pixel, we divide the total number of bits available (512 bytes * 8 bits/byte) by the total number of pixels (2048 pixels):

512 bytes * 8 bits/byte / 2048 pixels = 2 bits/pixel

Therefore, each pixel can be represented using 2 bits.

To calculate the maximum number of colors in the palette, we raise 2 (the number of possible values for each bit) to the power of the number of bits per pixel:

2^2 = 4

Therefore, the maximum number of colors in the palette for a 32x64 pixel image with 512 bytes of memory is 4.

Task 6: Maximum number of colors in a palette for a 128x128 pixel image with 4 kilobytes of memory

To determine the maximum number of colors in a palette for a 128x128 pixel image with 4 kilobytes of memory, we follow a similar approach as in Task 3.

Given that 4 kilobytes of memory are allocated for the image, and each pixel requires a certain number of bits to represent its color, we can calculate the number of bits available per pixel.

Since the image is 128x128 pixels, it contains a total of 128 * 128 = 16384 pixels.

To calculate the number of bits available per pixel, we divide the total number of bits available (4 kilobytes * 8 bits/kilobyte) by the total number of pixels (16384 pixels):

4 kilobytes * 8 bits/kilobyte / 16384 pixels = 2 bits/pixel

Therefore, each pixel can be represented using 2 bits.

To calculate the maximum number of colors in the palette, we raise 2 (the number of possible values for each bit) to the power of the number of bits per pixel:

2^2 = 4

Therefore, the maximum number of colors in the palette for a 128x128 pixel image with 4 kilobytes of memory is 4.