Why is my fixed-point number's FractionLength value greater than its WordLength value?

I create a fixed-point number with the following command

z=fi(-0.002)

and the following information appears

z =
 
   -0.0020

          DataTypeMode: Fixed-point: binary point scaling
                Signed: true
            WordLength: 16
        FractionLength: 23

             RoundMode: nearest
          OverflowMode: saturate
           ProductMode: FullPrecision
  MaxProductWordLength: 128
               SumMode: FullPrecision
      MaxSumWordLength: 128
         CastBeforeSum: true

The WordLength value is 16 bits, however, the FractionLength value seems to be 23 bits. Thus, there is some kind of error.

Answer 1

[MathWorks Support Team]

The terminology used in fixed-point math can be confusing, but it looks like there is nothing wrong with the FractionLength value, as it is not measured in terms of number of bits. The documentation at the following location discusses scaling of fixed-point values:

https://www.mathworks.com/help/releases/R2020b/fixedpoint/ug/fixed-point-numbers.html 

"fraction length" is defined to be the negative of the fixed exponent value. Thus, even though we are dealing with a 16-bit word length, there is no requirement for the fraction length to be less than 16.

The documentation at the following location discusses the concept of fraction length that is greater than word length or negative.

https://www.mathworks.com/help/releases/R2020b/dsp/ref/fixed-point-filter-properties.html 

Under the secton titled Property Details for Fixed Point Filter, there is a sub-section titled Notes About Fraction Length, Word Length, and Precision.