5.1.2.1 Q15 (1.15) Format

In Q15 format, the Most Significant bit is defined as a sign bit and the radix point is implied to lie just after the sign bit followed by the fractional value. This format is commonly referred to as 1.15 or Q15 format, where 1 is the number of bits used to represent the integer portion of the number, and 15 is the number of bits used to represent the fractional portion. The range of an N-bit two’s complement fraction with this implied radix point is -1.0 to (1 - 2^1-N). For a 16-bit fraction, the 1.15 data range is -1.0 (0x8000) to +0.999969482 (0x7FFF) with a precision of 3.05176x10^-5.

Figure 3: Fractional Format (16 bits)

The following table shows the conversion of a two’s complement 16-bit integer +24576 to Q15 value +0.75.

Table 5-1. Table1: Conversion of a Two’s Complement 16-Bit Integer to Q15
Binary		Dec		Q15
0	0 x (-2¹⁵)	0	0 x (-2⁰)	0

1	1 x 2¹⁴	16384	1 x 2^-1	0.5
1	1 x 2¹³	8192	1 x 2^-2	0.25
0	0 x 2¹²	0	0 x 2^-3	0
0	0 x 2¹¹	0	0 x 2^-4	0
0	0 x 2¹⁰	0	0 x 2^-5	0
0	0 x 2⁹	0	0 x 2^-6	0
0	0 x 2⁸	0	0 x 2^-7	0
0	0 x 2⁷	0	0 x 2^-8	0
0	0 x 2⁶	0	0 x 2^-9	0
0	0 x 2⁵	0	0 x 2^-10	0
0	0 x 2⁴	0	0 x 2^-11	0
0	0 x 2³	0	0 x 2^-12	0
0	0 x 2²	0	0 x 2^-13	0
0	0 x 2¹	0	0 x 2^-14	0
0	0 x 2⁰	0	0 x 2^-15	0
	SUM	+24576	SUM	+0.75
= Radix Point