InfoCompile

Range and Precision The  range  of a number gives the limits of the representation, while the  precision  gives the distance between successive numbers in the representation. The range and precision of a fixed-point number depend on the length of the word and the scaling. Range The following figure illustrates the range of representable numbers for an unsigned fixed-point number of size  ws , scaling  S , and bias  B . The following figure illustrates the range of representable numbers for a two's complement fixed-point number of size  ws , scaling  S , and bias  B  where the values of  ws , scaling  S , and bias  B  allow for both negative and positive numbers. For both the signed and unsigned fixed-point numbers of any data type, the number of different bit patterns is 2 ws . For example, if the fixed-point data type is an integer with scaling defined as  S = 1  and  B  = 0 , then the maximum unsigned value is  2 w s − 1 , because zero must be represen

Relationship Between Stored Integer Value and Real-World Value The binary encoding of variables is only an approximation of an arbitrarily precise real-world value. Therefore, the limitations of the binary representation automatically introduce limitations on the precision of the value. In  BinaryPoint  scaling, the relationship between the stored integer value and the real-world value is There is also  SlopeBias  scaling, which has the relationship where and https://blogs.mathworks.com/simulink/2008/12/14/representing-numbers-integers-and-fixed-point/ Fixed-Point Numbers: Binary Point Fixed-point numbers use the same integer representations, but they assign a different meaning to the bits.  We can introduce the idea of fractional bits and a binary point.  With integers, your smallest spacing between numbers is 1.  If we decide to let a bit represent ½ we now have closer spacing in our system.  The number of bits to the right of the binary