5.1.2.2 Q15.16 Format

In the Q15.16 format, the Most Significant bit is defined as a sign bit followed by 16 bits of the integral part. The radix point is implied to lie just after the integral part, followed by 16 bits of the fractional value. This format is commonly referred to as Q15.16 format. The range of Q15.16 numbers is from -32768.0 (0x8000 0000) to +32767.9999847412109375 (0x7FFF FFFF) and has a precision of 2-16.

Figure 4: Fractional Format (32 bits)

The following table shows the conversion of a two’s complement 32-bit integer, -715827882 to Q15.16 value -10922.6666564941.

Table 5-2. Table 2: Conversion of a Two’s Complement 32-Bit Integer to Q15.16
Binary Dec Q15.16
1 1 x (-231) -2147483648 1 x (-215) -32768
1 1 x 230 1073741824 1 x 214 16384
0 0 x 229 0 0 x 213 0
1 1 x 228 268435456 1 x 212 4096
0 0 x 227 0 0 x 211 0
1 1 x 226 67108864 1 x 210 1024
0 0 x 225 0 0 x 29 0
1 1 x 224 16777216 1 x 28 256
0 0 x 223 0 0 x 27 0
1 1 x 222 4194304 1 x 26 64
0 0 x 221 0 0 x 25 0
1 1 x 220 1048576 1 x 24 16
0 0 x 219 0 0 x 23 0
1 1 x 218 262144 1 x 22 4
0 0 x 217 0 0 x 21 0
1 1 x 216 65536 1 x 20 1
0 0 x 215 0 0 x 2-1 0
1 1 x 214 16384 1 x 2-2 0.25
0 0 x 213 0 0 x 2-3 0
1 0 x 212 4096 1 x 2-4 0.0625
0 0 x 211 0 0 x 2-5 0
1 1 x 210 1024 1 x 2-6 0.015625
0 0 x 29 0 0 x 2-7 0
1 1 x 28 256 1 x 2-8 0.00390625
0 0 x 27 0 0 x 2-9 0
1 1 x 26 64 1 x 2-10 0.000976563
0 0 x 25 0 0 x 2-11 0
1 1 x 24 16 1 x 2-12 0.000244141
0 0 x 23 0 0 x 2-13 0
1 1 x 22 4 1 x 2-14 6.10352E-05
1 1 x 21 2 1 x 2-15 3.01576E-05
0 0 x 20 0 0 x 2-16 0
SUM -715827882 SUM -10922.6666564941
= Radix Point