List of top Digital Logic Questions on Number Representations asked in GATE CS

The format of the single-precision floating-point representation of a real number as per the IEEE 754 standard is as follows: 
\[ \begin{array}{|c|c|c|} \hline \text{sign} & \text{exponent} & \text{mantissa} \\ \hline \end{array}\] Which one of the following choices is correct with respect to the smallest normalized positive number represented using the standard?

If \( x \) and \( y \) are two decimal digits and \( (0.1101)_2 = (0.8xy5)_{10} \), the decimal value of \( x + y \) is \(\underline{\hspace{2cm}}\).

Assume that a 12-bit Hamming codeword consisting of 8-bit data and 4 check bits is $d_8 d_7 d_6 d_5 c_8 d_4 d_3 d_2 c_4 d_1 c_2 c_1$, where the data bits and the check bits are given in the following tables. Which one of the following choices gives the correct values of $x$ and $y$?