Fixed Point Notation (in Register)

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As you know, fractional part of fixed point notation is can be different for different register. So, how is the fractional part determined according to the register bit address?

 8 bits =  1 sign bit + 4 bits  (integral) + 3 bits (fractional part)
16 bits =  1 sign bit + 9 bits  (integral) + 6 bits (fractional part)
32 bits =  1 sign bit + 15 bits (integral) + 9 bits (fractional part)

In here, for 32 bit register consist of "15 bit for integral part", "9 bit for fractional part", so if 128 bit register what will be happened? I searched to see if there was a formula for this, but I couldn't find the formula I wanted.

Also, another question is that, in programming language, example in C, is fixed point used any datatype? For example, "int16_t" data-type can be used for fractional part?

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