Texas Instruments TMS320C64X manual Fractional Q Formats, Table A−1. Q3.12 Bit Fields

Fractional Q Formats

A.2 Fractional Q Formats

Unless specifically noted, DSPLIB functions use Q15 format, or to be more exact, Q0.15. In a Qm.n format, there are m bits used to represent the two’s complement integer portion of the number, and n bits used to represent the two’s complement fractional 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 (−2m,2m) and the finest fractional resolution is 2−n.

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 format 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.

A.2.1 Q3.12 Format

Q.3.12 format places the sign bit after the fourth binary digit from the right, and the next 12 bits contain the two’s complement fractional component. The approximate allowable range of numbers in Q.3.12 representation is (−8,8) and the finest fractional resolution is 2−12 = 2.441 × 10−4.

Table A−1. Q3.12 Bit Fields

Bit	15	14	13	12	11	10	9	…	0
Value	S	I3	I2	I1	Q11	Q10	Q9	…	Q0

A.2.2 Q.15 Format

Q.15 format places the sign bit at the leftmost binary digit, and the next 15 leftmost bits contain the two’s complement fractional component. The approximate allowable range of numbers in Q.15 representation is (−1,1) and the finest fractional resolution is 2−15 = 3.05 × 10−5.

Table A−2. Q.15 Bit Fields

Bit	15	14	13	12	11	10	9	…	0
Value	S	Q14	Q13	Q12	Q11	Q10	Q9	…	Q0

Performance/Fractional Q Formats A-3