All digital imagery must be expressed in binary format, a two digit numbering system consisting of 0 and 1. Since there are only two possibilities using just 0 and 1, we must use numbers containing more than one combination of the two numbers (e.g., 01, 101, 11101). In this way, we can get more than two possible combinations for each number. We can relate how many possible combinations exist in a binary number to the number of digits by the following:
#combinations = 2 to the N power
where N is the number of digits in a binary number.
So for a two digit binary number, there are 4 possible combinations. For a 3 digit number there are 8 combinations and so on. When a binary file is viewed as an image, each binary number is viewed as a single pixel and the length of each number defines the number of possible combinations. Each combination can define a single gray shade ranging from black to white. When you hear of something called a 6 bit image, it means that each pixel is represented by a binary number 6 digits long with 64 gray shades. When viewing the actual pixel values, we often convert the binary numbers to base 10 numbers for easy viewing. Upon doing so, the darkest (lightest) gray shade is represented by a pixel value of 0 (64) for a 6 bit image.
For your satisfaction, figure out the number of gray shades for a 10 bit image. The NOAA polar orbiters and the latest GOES satellites transmit imagery with this number of gray shades.