This question is poorly framed and has interpretation ambiguity. Refer to the discussion on this question in the below link :
https://cs.stackexchange.com/questions/135713/representation-of-unsigned-integer-on-a-little-endian-big-endian-computer
All kinds of “interpretations” are available in that discussion.
The following is my interpretation of the question :
It is asking “which of the following choices represent(s) the unsigned integer on a little-endian computer?”
Take Option $``\mathtt{0x6665}” :$
It is saying that $\mathtt{0x6665}$ is the representation of an integer on a little-endian computer, so, it means that the original number must have been $\mathtt{0x6566}.$
So, for the original number $\mathtt{0x6566} :$
- On little endian(LE) $: \mathtt{0x6665}$
- On Big endian(BE) $: \mathtt{0x6566}$
Clearly, $LE = 255 + BE$
Similarly, for $\mathtt{0x0100}.$
Take $\mathtt{0x0100} :$
It is saying that $\mathtt{0x0100}$ is the representation of an integer on a little-endian computer, so, it means that the original number must have been $\mathtt{0x0001}. $
So, for the number $\mathtt{0x0001} :$
- On little endian(LE) $: \mathtt{0x0100}$
- On Big endian(BE) $: \mathtt{0x0001}$
Clearly,$ LE = 255 + BE$
Similarly for $\mathtt{0x4243}$ and $\mathtt{0x0001},$ They do not satisfy $``LE = 255 + BE \;”$, So, answer is option A,D.
Refer to Slide 26 in the below article :
Nice Reference: https://www.cs.utexas.edu/~byoung/cs429/slides2-bits-bytes.pdf
$\textbf{Representing Integers:}$
int A = 15213;
int B = -15213;
long int C = 15213;
$$\qquad 15213_{10} = 0011101101101101_{2} = \text{3B6D}_{16}$$
$$\begin{array}{|c| c | c | c| } \hline & \textbf{Linux (little endian)} & \textbf{Alpha (little endian)} & \textbf{Sun (big endian)} \\\hline \mathtt{A} & \mathtt{6D \; 3B \; 00 \; 00} & \mathtt{6D\;3B\;00\;00} & \mathtt{00\;00\;3B\;6D} \\\hline \mathtt{B} & \mathtt{93\;C4\;FF\;FF} & \mathtt{93\;C4\;FF\;FF} & \mathtt{FF\; FF\; C4\;93} \\\hline \mathtt{C} & \mathtt{6D\;3B\;00\;00\;00\;00\;00\;00} & \mathtt{6D\;3B\;00\;00\;00\;00\;00\;00} & \mathtt{00\;00\;00\;00\;00\;00\;3B\;6D} \\\hline \end{array}$$ $\textbf{Byte Ordering Examples:}$
- $\text{Big Endian:}$ Most significant byte has lowest (first) address.
- $\text{Little Endian:}$ Least significant byte has lowest address.
$\text{Example:}$
- Int variable $\mathtt{x}$ has $4$-byte representation $\mathtt{0x01234567}.$
- Address gives by $\mathtt{\&x}$ is $\mathtt{0x100}.$
$\text{Big Endian:}$
$\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline \textbf{Address:} & \quad & \quad & \mathtt{0x100} & \mathtt{0x101} & \mathtt{0x102} & \mathtt{0x103} & & \\\hline \textbf{Value:} &\quad & \quad & 01 & 23 & 45 & 67 & \quad & \quad \\\hline \end{array}$
$\text{Little Endian:}$
$\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline \textbf{Address:} & \quad & \quad & \mathtt{0x100} & \mathtt{0x101} & \mathtt{0x102} & \mathtt{0x103} & & \\\hline \textbf{Value:} &\quad & \quad & 67 & 45 & 23 & 01 & \quad & \quad \\\hline \end{array}$
Note that different people are having different interpretations of this question. I have asked this question on cs.StackExchange, and you can read the discussion in the below link :
https://cs.stackexchange.com/questions/135713/representation-of-unsigned-integer-on-a-little-endian-big-endian-computer