The format of the single-precision floating-point representation of a real number as per the IEEE 754 standard is as follows: Which one of the following choices is correct with respect to the $smallest$ normalized positive number represented using the standard?

In the IEEE 754 single-precision (32-bit) floating-point format:

• Sign bit ($S$): 1 bit

• Biased Exponent ($E$): 8 bits

• Fraction/Mantissa ($M$): 23 bits

For normalized numbers:

• The biased exponent $E$ ranges from $1$ to $254$ ($E = 00000001_2$ to $11111110_2$). $E = 0$ is reserved for subnormal numbers and zero, while $E = 255$ is reserved for $\pm\infty$ and NaN.

• The real value represented is given by:

  $$(-1)^S \times 2^{E - 127} \times (1.M)_2$$

To represent the smallest normalized positive number:

1. The sign bit is $S = 0$ (positive).

2. The exponent $E$ must be the smallest non-zero exponent: $E = 1$ ($00000001_2$).

3. The mantissa $M$ must be the smallest possible fraction: all zeros, i.e., $M = 00000000000000000000000_2$.

This gives the value:

Hence, $\text{exponent} = 00000001$ and $\text{mantissa} = 00000000000000000000000$, which corresponds to Option C.