Photoshop was the first image editor to edit 16 bit raw files from $10,000 digital still cameras. If your camera cost $10,000 dollars then you will not mind spending $1,000 on an image editing program plus hundreds of dollars every year for updates. For everyone else there is Gimp.
You can download gimp free from http://www.gimp.org/.
Start with a good book on Gimp, Beginning Gimp and work your way through the examples so you will know all the right steps when you next edit an image.
Colour (color in USA) depth is a measure of the range of colours that can be carried in an image file. Our eyes see about 12 million colours. A good display screen can display 24 million. Cheap LCD screens might display only 65 thousand colours. The 24 million colours on your screen are from 24 bit colour divided into red, green, and blue with each colour having 8 bits of colour information. Digital camera makers refer to the number of bits in a colour as color depth (yes they all speak American). Your screen is 24 bit colour in computer terms but 8 bit color depth in camera specifications.
16 bit color depth is the ideal for professional cameras with professional cameras currently delivering only 14 bit and 12 bit. You lose some bits of information when processing images to remove wrinkles, haze, and other problems. If you start with 8 bit, you end up with only 7 or 6 or 5 bits of useful depth. Starting with 12 or more gives you the margin to work on the image and still end up with 8 bits of detail.
Gimp 2.8 can import 16 bit raw files from cameras and perform a few functions in 16 bit mode during the importation but the internal storage of images is still 8 bit. Professional cameras tend to be 12 bit, even if they produce 16 bit files, and the overall loss is not much in a good image. You find the extra bits of most use in high contrast wedding photographs where an 8 bit camera either drops all detail in large areas of black or drops all detail in the bright white areas or squashes the skin tones down while trying to preserve detail in the dark and light areas. A 12 bit raw file gives your camera the extra space to record more detail and you can include the extra detail by adjusting the blacks and whites during import. For some photographs, you may want to adjust the images further to bring out light colours in some regions and dark colours in other regions, a task that needs the Photoshop 16 bit mode.
GIMP 2 for Photographers is a recent book on Gimp with a chapter on the new Gimp 16 bit import feature. Consider buying Gimp 2 for Photographers: Image Editing with Open Source Software if you have a 12 or 16 bit camera.
CinePaint is an alternative to Gimp for 16 bit colour but only if you use Linux. CinePaint was based an old version of Gimp rewritten for editing movie images and is independently maintained. Advances in CinePaint include 16 bit and 32 bit colour depth.
If you are not absolutely full time one hundred percent focused on professional editing of images, then use Gimp instead of Photoshop or Paint Shop Pro.