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
BinaryDecQ15.16
11 x (-231)-21474836481 x (-215)-32768
11 x 23010737418241 x 21416384
00 x 22900 x 2130
11 x 2282684354561 x 2124096
00 x 22700 x 2110
11 x 226671088641 x 2101024
00 x 22500 x 290
11 x 224167772161 x 28256
00 x 22300 x 270
11 x 22241943041 x 2664
00 x 22100 x 250
11 x 22010485761 x 2416
00 x 21900 x 230
11 x 2182621441 x 224
00 x 21700 x 210
11 x 216655361 x 201
00 x 21500 x 2-10
11 x 214163841 x 2-20.25
00 x 21300 x 2-30
10 x 21240961 x 2-40.0625
00 x 21100 x 2-50
11 x 21010241 x 2-60.015625
00 x 2900 x 2-70
11 x 282561 x 2-80.00390625
00 x 2700 x 2-90
11 x 26641 x 2-100.000976563
00 x 2500 x 2-110
11 x 24161 x 2-120.000244141
00 x 2300 x 2-130
11 x 2241 x 2-146.10352E-05
11 x 2121 x 2-153.01576E-05
00 x 2000 x 2-160
SUM-715827882SUM-10922.6666564941
= Radix Point