For normal images the range of shades of gray is from 0 to 256, what is it for Dicom CT monochrome images?
Techically, I agree with Amit Joshi. But especially for CT images you will usually find a grayscale range expressed in Hounsfield Units. These range from -1000 to +4000. By applying a linear transformation of the pixel data as specified by the attributes Rescale Intercept (0028,1052) and Rescale Slope (0028,1053), pixel data as described by Amit Joshi's anwer are mapped to that range.
To this range, the windowing (VOI LUT) funtion is applied.
[EDIT] A little explanation on Hounsfield units (HU)...
HU are valid for CT images only. A range of HU corresponds to a particular type of tissue or depicted structures, e.g.
-1000 -> air
0 -> fat
10-40 -> kidney
and so on.
So in CT images, pixel values found in the file are usually mapped to HU using Rescale Slope and -Intercept. Whether or not the this is the case is indicated by the attribute Rescale Type (0028,1054). HUs are not only used for measuring grayvalues and deducing tissue type from the median value but also for windowing. In CT, you refer to "bone window", "tissue window" etc.
So the relevant part of the DICOM Grayscale Standard Display Function (GSDF, see PS3.14) is: