The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is gate computer science 2017

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The n-bit fixed-point representation of an unsigned real number X uses f bits for the fraction part. Let i = n - f. The range of decimal values for X in this representation is :- -gate computer science 2017

A) 2^-f
B) 2^-f to ( 2^i - 2^-f)
C) 0 to 2^-i
D) 0 to (2^i -2^-f)


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Answers

D) 0 to (2^i-2^-f)

Explanation: 
Since given number is in unsigned bit representation, its decimal value starts with 0. 
We have i bit in integral part so maximum value will be 2i 
Thus integral value will be from 0 to 2i - 1
We know fraction part of binary representation are calculated as (1/0)*2-f 
Thus with f bit maximum number possible = sum of GP series with a = 1/2 and r = 1/2
Thus fmax = {1/2(1 – (1/2)^f}/(1 – 1/2)
                = 1 – 2^-f
Thus maximum fractional value possible = 2^i – 1 + (1 – 2^-f )
                                       = 2^i - 2^-f

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