> And you could have another dimmer that goes between exactly the same two levels of lightness. The same range. but with 1,000,000 steps in between. The range of the two dimmer switches is the same. They both go from the same minimum to the same maximum.
The thing is that you can't set the minimum value arbitrarily, because the scale is anchored to zero. So "1" is always one step above zero, and the step size is a function of bit depth.
So going with our example here, a dimmer with 1000000 steps would not have the same range as dimmer with 8 steps, because the the minimum brightness of one is 1/1000000th of max, and 1/8th of the max for the other (assuming linear scale for simplicity's sake, the principle applies to nonlinear scales too)
You could have a dimmer that goes from one level of lightness, up to another, with 8 steps in between. And you could have another dimmer that goes between exactly the same two levels of lightness. The same range. but with 1,000,000 steps in between. The range of the two dimmer switches is the same. They both go from the same minimum to the same maximum. Just the number of steps in between is different. The number of bits represents the number of steps.
Why is 1,000,000 steps the required number? 1,000,000 is just the number of integral factors in the range in base 10. But why is an integral factor more important than a fractional one? They could both be perceptible to a human. The range is the same in both cases, and the given explanation was given that the range was so high.