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 fixedpoint number depend on the length of the word and the scaling.
The following figure illustrates the range of representable numbers for an unsigned fixedpoint number of size ws, scaling S, and bias B.
The following figure illustrates the range of representable numbers for a two's complement fixedpoint 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 fixedpoint numbers of any data type, the number of different bit patterns is 2^{ws}.
For example, if the fixedpoint data type is an integer with scaling defined as $$S=1$$ and B = 0, then the maximum unsigned value is $${2}^{ws1}$$, because zero must be represented. In two's complement, negative numbers must be represented as well as zero, so the maximum value is $${2}^{ws1}1$$. Additionally, since there is only one representation for zero, there must be an unequal number of positive and negative numbers. This means there is a representation for $${2}^{ws1}$$ but not for $${2}^{ws1}$$.
The precision of a data type is given by the slope. In this usage, precision means the difference between neighboring representable values.
The low limit, high limit, and default binarypointonly scaling for the supported fixedpoint data types discussed in BinaryPointOnly Scaling are given in the following table. SeeLimitations on Precision and Limitations on Range for more information.
FixedPoint Data Type Range and Default Scaling
Name  Data Type  Low Limit  High Limit  Default Scaling (~Precision) 

Unsigned Integer 
 0  $${2}^{ws}1$$ 

Signed Integer 
 $${2}^{ws1}$$  $${2}^{ws1}1$$ 

Unsigned Binary Point 
 0  $$({2}^{ws}1){2}^{fl}$$  $${2}^{fl}$$ 
Signed Binary Point 
 $${2}^{ws1fl}$$  $$({2}^{ws1}1){2}^{fl}$$  $${2}^{fl}$$ 
Unsigned Slope Bias 

 $$s({2}^{ws}1)+b$$  s 
Signed Slope Bias 
 $$s({2}^{ws1})+b$$  $$s({2}^{ws1}1)+b$$  s 
s = Slope, b = Bias, ws = WordLength, fl = FractionLength
The precisions, range of signed values, and range of unsigned values for an 8bit generalized fixedpoint data type with binarypointonly scaling are listed in the follow table. Note that the first scaling value (2^{1}) represents a binary point that is not contiguous with the word.
Scaling  Precision  Range of Signed Values (Low, High)  Range of Unsigned Values (Low, High) 

2^{1}  2.0  256, 254  0, 510 
2^{0}  1.0  128, 127  0, 255 
2^{1}  0.5  64, 63.5  0, 127.5 
2^{2}  0.25  32, 31.75  0, 63.75 
2^{3}  0.125  16, 15.875  0, 31.875 
2^{4}  0.0625  8, 7.9375  0, 15.9375 
2^{5}  0.03125  4, 3.96875  0, 7.96875 
2^{6}  0.015625  2, 1.984375  0, 3.984375 
2^{7}  0.0078125  1, 0.9921875  0, 1.9921875 
2^{8}  0.00390625  0.5, 0.49609375  0, 0.99609375 
The precision and ranges of signed and unsigned values for an
8bit fixedpoint data type using slope and bias scaling are listed
in the following table. The slope starts at a value of 1.25
with
a bias of 1.0
for all slopes. Note that the slope
is the same as the precision.
Bias  Slope/Precision  Range of Signed Values (low, high)  Range of Unsigned Values (low, high) 

1  1.25  159, 159.75  1, 319.75 
1  0.625  79, 80.375  1, 160.375 
1  0.3125  39, 40.6875  1, 80.6875 
1  0.15625  19, 20.84375  1, 40.84375 
1  0.078125  9, 10.921875  1, 20.921875 
1  0.0390625  4, 5.9609375  1, 10.9609375 
1  0.01953125  1.5, 3.48046875  1, 5.98046875 
1  0.009765625  0.25, 2.240234375  1, 3.490234375 
1  0.0048828125  0.375, 1.6201171875  1, 2.2451171875 