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

In an unsigned fixed-point representation with $n$ total bits, $i = n - f$ integer bits, and $f$ fractional bits:

• Minimum value: When all $n$ bits are $0$, the value is:

  $$X_{\min} = 0$$

• Maximum value: When all $n$ bits are $1$, the value is:

  $$X_{\max} = \sum_{k=0}^{i-1} 2^k + \sum_{j=1}^f 2^{-j} = (2^i - 1) + (1 - 2^{-f}) = 2^i - 2^{-f}$$

Alternatively, representing the $n$-bit number as an integer value $M \in [0, 2^n - 1]$ scaled by $2^{-f}$:

Hence, the range of decimal values is $0$ to $(2^i - 2^{-f})$, which matches option (D).