Problem $1$: Data Packet Analysis and Precision

Imagine you are a software engineer working on a system that processes data packets from a remote weather monitoring sensor$.$ Each data packet from the sensor contains a $32-$bit binary sequence, which can be interpreted in multiple ways depending on the type of information being sent. Your task is to decode the packet below:

Binary Sequence:

$01001000011001010110110001101100$

The packet could represent: A $32-$bit unsigned integer, which encodes a sensor reading and an ASCII message containing four characters describing the sensor$\text{'}$s state.

Integer Interpretation

If the sequence represents a $32-$bit unsigned integer, what is the value?

$2.$ Sensor Status Interpretation $($ASCII Characters$)$

If the packet represents sensor status, convert each byte to its corresponding ASCII character. Write down the characters and their respective codes. What message is represented?

$3.$ Understanding Floating$-$Point Precision

In floating$-$point arithmetic, certain expressions may not yield the exact expected result due to precision limitations$.$ For instance, evaluating $0\mathrm{.}1+0\mathrm{.}2==0\mathrm{.}3$ often results in false, even though logically$,$ we expect it to be true.

Explain why this happens. Describe how floating$-$point numbers are stored in memory using the IEEE $754$ standard and why adding $0\mathrm{.}1$ and $0\mathrm{.}2$ does not yield exactly $0\mathrm{.}3.$ Highlight the role of binary fractions and rounding errors in your explanation.