With digital cameras, many photographers are using an exposure method called "Expose to the right" or ETTR.
In the "Using the Histogram on digital cameras" section, you would have learned about keeping the histogram centered and not "blocking up" on either side.
With ETTR you would keep the histogram as far to the right as it can get without blocking up. This makes the image as bright as possible without going too far.
One of the effects of having too low an exposure on digital cameras is that it creates noise (random pixels) - especially in the shadow areas.
To use the ETTR method, make sure there is no gap to the right side of the histogram and that it is not "piled up" on the right.
If you have not seen the "Using the Histogram on digital cameras" please review it now.