A color system of RGB each of them has a brightness value fr

A color system of R,G,B, each of them has a brightness value from 0-60 inslusively. (i) how many colors in this system? (ii)how many bots are needed to represent a color?(iii) if I cannot choose a level below 10 for all three RGB at the same time, how does this change question part(i)?

Please help me. For (i) my answer is 61*61*61. But I dont know (ii)&(iii). Thanks.

Solution

Given, the color system of RGB each has a brightness values in range 0 - 60. That is each parameter has 61 possible values.

(i) how many colors in this system?

Out 61 various brightnesses, you have to select 1. That is: ⁶¹C₁ possibilities. = 61. And to select 1 among 61 for each color Red, Blue, and Green, it total possible colors are: 61 x 61 x 61 = 226,981 different colors are possible in the system.

(ii)how many bits are needed to represent a color?

To represent 61 different values, you need to represent a total of 6 bits. Using 6 bits you can represent a total of 2⁶ = 64 different values. And therefore, 6 bits are required to represent each variant.

And to represent R, G, B together, you need 6 + 6 + 6 = 18 bits. 18 bits together are required to represent 61 variants of each color, together of 226,981 shades.

(iii) if I cannot choose a level below 10 for all three RGB at the same time, how does this change question part(i)?

You cannot choose a level below 10 for all three RGB at the same time.

So, the number of colors in this system is:

The total possible shades such that all the three colors has brightnesses below 10(0 - 9) are: 10 x 10 x 10 = 1000.

And these 1000 colors are excluded from the total possible colors. Therefore, on imposing this constraint, the palette will now have a total of 226,981 - 1000 = 225,981 shades.