GATE CS 2021 Set 2 Q44 — Number Representations (Fixed and Floating Point)

Let the 2-byte unsigned integer be stored in memory at consecutive byte addresses $A$ and $A+1$ as bytes $X$ and $Y$ respectively.

• On a Little Endian computer, the least significant byte (LSB) is stored at the lower address $A$. Thus, the value is: $$V_{LE} = Y \cdot 256 + X$$
• On a Big Endian computer, the most significant byte (MSB) is stored at the lower address $A$. Thus, the value is: $$V_{BE} = X \cdot 256 + Y$$

According to the problem, the value on the little endian computer is $255$ more than that on the big endian computer:

This means the most significant byte ($Y$) must be exactly $1$ greater than the least significant byte ($X$). Let us evaluate the options represented as $0\text{x}YX$:

• Option A ($0\text{x}6665$): $Y = 0\text{x}66$, $X = 0\text{x}65$. Here, $Y - X = 0\text{x}66 - 0\text{x}65 = 1$. (Correct)
• Option B ($0\text{x}0001$): $Y = 0\text{x}00$, $X = 0\text{x}01$. Here, $Y - X = -1$. (Incorrect)
• Option C ($0\text{x}4243$): $Y = 0\text{x}42$, $X = 0\text{x}43$. Here, $Y - X = -1$. (Incorrect)
• Option D ($0\text{x}0100$): $Y = 0\text{x}01$, $X = 0\text{x}00$. Here, $Y - X = 1 - 0 = 1$. (Correct)