To store a 64 x 64 pixel raster image, 1024 KB of memory was allocated.

To store a 64 x 64 pixel raster image, 1024 KB of memory was allocated. What is the maximum possible number of colors in the image palette?

Formula for finding colors in the palette: i = (x * y) / I, where x and y are the resolution;

Now we substitute the data for us values in the formula: i = 64 x 64/1024 KB;

64 is 2 to the 6th power, that is, we get i = 2 ^ 12 (according to the rule of addition of powers) / 1024 KB;

1024 is 2 to the 10th power, that is, we get i = 2 ^ 12/2 ^ 10;

According to the rule of dividing degrees with the same bases i = 2 ^ 2 – this is equal to 4;

Now you need to find the maximum number of colors that is N = 2 ^ i;

Substitute i in this formula and calculate N = 2 ^ 4 = 16;

Answer: 16.