https://en.wikipedia.org/wiki/Q_(number_format)
Q is a fixed point number format where the number of fractional bits (and optionally the number of integer bits) is specified. For example, a Q15 number has 15 fractional bits; a Q1.14 number has 1 integer bit and 14 fractional bits. Q format is often used in hardware that does not have a floating-point unit and in applications that require constant resolution.
Q format numbers are notionally fixed point numbers, that is, they are stored and operated upon as regular binary signed integers, thus allowing standard integer hardware/ALU to perform rational number calculations. The number of integer bits, fractional bits and the underlying word size are to be chosen by the programmer on an application-specific basis — the programmer's choices of the foregoing will depend on the range and resolution needed for the numbers.
Some DSP architectures offer native support for common formats, such as Q1.15. In this case, the processor can support arithmetic in one step, offering saturation (for addition and subtraction) and renormalization (for multiplication) in a single instruction. Most standard CPUs do not. If the architecture does not directly support the particular fixed point format chosen, the programmer will need to handle saturation and renormalization explicitly with bounds checking and bit shifting.
There are two conflicting notations for fixed point. Both notations are written as Qm.n, where:
One convention includes the sign bit in the value of m,[1] and the other convention does not. The choice of convention can be determined by summing m+n. If the value is equal to the register size, then the sign bit is included in the value of m. If it is one less than the register size, the sign bit is not included in the value of m.
In addition, the letter U can be prefixed to the Q to indicate an unsigned value, such as UQ1.15, indicating values from 0.0 to +1.99997.
Signed Q values are stored in two's complement format, just like signed integer values on most processors. In two's complement, the sign bit is extended to the register size.
For a given Qm.n format, using an m+n+1 bit signed integer container with n fractional bits:
For a given UQm.n format, using an m+n bit unsigned integer container with n fractional bits:
For example, a Q14.1 format number:
Unlike floating point numbers, the resolution of Q numbers will remain constant over the entire range.