For example, the specification Q3.12 describes a signed binary fixed-point number with a w = 16 bits in total, comprising the sign bit, three bits for the integer part, and 12 bits that are assumed to be fraction. That is, a 16-bit signed (two's complement) integer, that is implicitly multiplied by the scaling factor 2−12
In particular, when n is zero, the numbers are just integers. — If m is zero, all bits except the sign bit are fraction bits; then the range of the stored number is from −1.0 (inclusive) to +1 (exclusive). Both m and n may be negative
The m and the dot may be omitted, in which case they are inferred from the size of the variable or register where the value is stored. Thus Q12 means a signed integer with any number of bits, that is implicitly multiplied by 2−12.
The letter U can be prefixed to the Q to denote an unsigned binary fixed-point format. For example, UQ1.15 describes values represented as unsigned 16-bit integers with implicit scaling factor of 2−15, which range from 0.0 to (216−1)/215 = +1.999969482421875.
The resolution (difference between successive values) of a Qm.n or UQm.n format (both used AMD convention) is always 2−n. The range of representable values is
For example, a Q15.1 format number requires 15+1 = 16 bits, has resolution 2−1 = 0.5, and the representable values range from −214 = −16384.0 to +214 − 2−1 = +16383.5. In hexadecimal, the negative values range from 0x8000 to 0xFFFF followed by the non-negative ones from 0x0000 to 0x7FFF.