Feel free to check out the guide that we have prepared to help you in this problem.

For the following question, we will be following the IEEE$-754$ Floating Point standard but with different numbers of bits: with $6$ bits of exponent, an exponent bias of $-31,$ and $25$ bits of mantissa. Due to PrairieLearn restrictions, please submit your answer as the full number.

Floating point representations present a trade$-$off between range and accuracy. Due to the limited significant digits that you can represent, there will be a point where integers cannot be exactly represented anymore.

Q$1\mathrm{.}1$: What's the smallest non$-$infinite positive integer $($whole number$)$ this representation CANNOT represent?

Hint: When the step size becomes $2,$ you start skipping whole numbers.