This computer will have 64 colors (2bits red, 2 bits green, 2 bits blue).

I was curious what the colors would look like, so I made a kind of three-dimensional plot with dimensions red, green and blue. It became a cube, built from 64 small bricks. If we look at the cube with the black brick pointing to us, we see this:

So, starting from the black brick going to the right, we see increase in the red component. To the left, we see increase in blue component, and from black going down we see increase in green component. At the circumference we see the bright rainbow colors, and the remaining colors are darker versions of the colors.

At the opposite side of the cube (unvisible in the above picture), we have a point where the amount of all primary colors is maximal. That is the color white. If we look at the other side of the cube we see this:

At the circumference we see the same bright rainbow colors again. The remaining bricks are the lighter versions of the rainbow colors.

But we did not see everything ! At the inside of the cube, there are 8 bricks that we didn't see yet. These are light-grey, dark-grey, and a grayish version of the primary colors:

So here we see the eight hidden bricks, shown from both sides.

The following table shows these colors, numbered from 0 to 63, and also with their hexadecimal web color. The first column has the grayish colors, and black, white and the two greys are at the bottom:

So this table will be a help if I ever come so far to program colored stuff for my contraption.