Determine the Range of Fixed-Point Numbers
Fixed-point variables have a limited range for the same reason they have limited precision — because digital systems represent numbers with a finite number of bits. As a general example, consider the case where an integer is represented as a fixed-point word of size ws. The range for signed and unsigned words is given by
Using the general [Slope Bias] encoding scheme described in Scaling, the approximate real-world value has the range
If the real-world value exceeds the limited range of the approximate value, then the accuracy of the representation can become significantly worse.