what word lenght is used o represent a binary code of 1000 shades of colour?

111110100

Hmmm. This has been answered by every computer manufacturer in the world... First, let's deal with shades of grey - 2000 shades needs 2^n bits, or 2^n > 2000... 2*11 = 2048, so we need 11 bits for 2^ 11 "different" things. BUT, we need 3 colors (RGB, Red, Green, Blue), or 2^33 bits for full 2000 shades of color in each subcolor... BUT, for just 2000 shades of total color, we do the same calculation after taking the cube root of 2,000 = 12.6, so 11 bits (2^11=2048) is enough to produce 2000 different shades of color. So, with 11 bits, you can represent 200 different shades of color information.