An uncompressed bitmap with a size of 64×512 pixels takes up 32 KB of memory.

To solve this problem, you first need to determine the total number of pixels in this image.

We multiply its sizes among ourselves.

64 * 512 = 32768 pixels.

We translate the specified information volume of the image into bits.

Since 1 KB contains 1024 bytes, and 1 byte contains 8 bits, we get:

32 * 1024 * 8 = 32 * 8192 = 262144 bits.

Find the information volume of one pixel in the image.

We divide the amount of information by the number of pixels.

262144/32768 = 8 bits.

From this it follows that the color palette will contain:

N = 28 = 256 colors.

Answer:

256 colors.