Fractional Q Formats; Format; A.2 Fractional Q Formats - Texas Instruments TMS320C67 DSP Series Programmer's Reference Manual

A.2 Fractional Q Formats

A.2.1 Q.15 Format
Table A-1. Q.15 Bit Fields
Unless specifically noted, DSPLIB functions use IEEE floating point format.
But few of the functions make use of fixed-point Q0.15 format also. In a Qm.n
format, there are m bits used to represent the two's complement integer por-
tion of the number, and n bits used to represent the two's complement fraction-
al portion. m+n+1 bits are needed to store a general Qm.n number. The extra
bit is needed to store the sign of the number in the most-significant bit position.
The representable integer range is specified by (-2
- n
tional resolution is 2
For example, the most commonly used format is Q.15. Q.15 means that a
16-bit word is used to express a signed number between positive and negative
one. The most-significant binary digit is interpreted as the sign bit in any Q for-
mat number. Thus, in Q.15 format, the decimal point is placed immediately to
the right of the sign bit. The fractional portion to the right of the sign bit is stored
in regular two's complement format.
Q.15 format places the sign bit at the leftmost binary digit, and the next 15 left-
most bits contain the two's complement fractional component. The approxi-
mate allowable range of numbers in Q.15 representation is (-1,1) and the fin-
est fractional resolution is 2
Bit 15 14
Value S Q14
.
= 3.05 × 10
- 15 - 5
13 12 11
Q13 Q12 Q11
Performance/Fractional Q Formats

Fractional Q Formats

m m
,2 ) and the finest frac-
.
...
10 9
...
Q10 Q9
0
Q0
A-3