Q (number format)

The Q notation is a way to specify the parameters of a binary fixed point number format. Specifically, how many bits are allocated for the integer portion, how many for the fractional portion, and whether there is a sign-bit.

For example, in Q notation, Q7.8 means that the signed fixed point numbers in this format have 7 bits for the integer part and 8 bits for the fraction part. One extra bit is implicitly added for signed numbers. Therefore, Q7.8 is a 16-bit word, with the most significant bit representing the two's complement sign bit.

Q7.8

Sign bit

7-bit integer

8-bit fraction

Bit Value

${\displaystyle -2^{7}}$

${\displaystyle 2^{6}}$

${\displaystyle 2^{5}}$

${\displaystyle 2^{4}}$

${\displaystyle 2^{3}}$

${\displaystyle 2^{2}}$

${\displaystyle 2^{1}}$

${\displaystyle 2^{0}}$

${\displaystyle 2^{-1}}$

${\displaystyle 2^{-2}}$

${\displaystyle 2^{-3}}$

${\displaystyle 2^{-4}}$

${\displaystyle 2^{-5}}$

${\displaystyle 2^{-6}}$

${\displaystyle 2^{-7}}$

${\displaystyle 2^{-8}}$

There is an ARM variation of the Q notation that explicitly adds the sign bit to the integer part. In ARM Q notation, the above format would be called Q8.8.

A number of other notations have been used for the same purpose.