Question

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?

• A. exponent = 00000000 and mantissa = 00000000000000000000000
• B. exponent = 00000000 and mantissa = 00000000000000000000001
• C. exponent = 00000001 and mantissa = 00000000000000000000000
• D. exponent = 00000001 and mantissa = 00000000000000000000001

Hint:

Exponent all zeros indicate denormalized numbers; normalized numbers always have a non-zero exponent.

Answer 1

The Correct Option is C

Step 1: Recall IEEE 754 normalization rule.
In IEEE 754 single precision, normalized numbers have a non-zero exponent field and an implicit leading 1 in the mantissa.

Step 2: Identify smallest normalized exponent.
The smallest exponent for a normalized number is \texttt{00000001}. The exponent \texttt{00000000} is reserved for denormalized numbers.

Step 3: Determine smallest mantissa.
The smallest normalized value uses all zeros in the mantissa, since the implicit leading 1 already exists.

Step 4: Conclusion.
Thus, the smallest normalized positive number has exponent \texttt{00000001} and mantissa all zeros.

Final Answer: (C)