5.1.3 Integer - Fractional Format Mapping

The same twos complement N-bit word may represent an integer format value or a fractional format value. For example., the 16-bit integer range [-32768, +32767] format maps to Q15 range of [-1.0, +0.999969482]. The following figure shows the mapping between these formats.

Figure 5-2. Mapping between 16-bit integer format and Q15 fractional format

A similar relationship exists between the 32-bit integer format and the Q15.16 format, where the integer range [-2147483648, +2147483647] is mapped to the Q15.16 range [-32768.0, +32767.9999847412109375].

Figure 5-3. Mapping between 32-bit integer format and Q15.16 format

This relationship also exists between the 32-bit integer format and the Q31 format, where the integer range [-2147483648, +2147483647] is mapped to the Q31 range [-1, 0.99999999954343387].

Figure 5-4. Mapping between 32-bit integer format and Q31 format