fixed point precision

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Peace!
I want ask about the number of bits shoud I use in an fixed_point number 
to obtein the good precision, precision of distance eclidean.
some detail:
I want to determine an vector of foor element VECT[MOY1,MOY2,MOY3,MOY4], 
each element is the moyen of one quart of matrix of (64*64), the matrix' 
element value varies (0-255)'''it's pixel valor'''
--> the result of division (MOY1=SUM/Nbits) has 8 bits in the integer 
part;
Question: how many bits of fractional part shout I use to get the good 
result (result of euclidean distance between two vector 
VECT1[MOY11,MOY12,MOY13,MOY14] and VECT[MOY21,MOY22,MOY23,MOY24])..
thank you....peace:

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