GATE CS 2017 Set 2 Q1 — Number Representations (Fixed and Floating Point)

To convert the $16\text{-bit}$ unsigned integer $X$ from hexadecimal to octal, we can first convert it to binary and then group the binary digits into sets of three.

Step 1: Convert Hexadecimal to Binary
Each hexadecimal digit corresponds to a $4\text{-bit}$ binary representation:

• $\text{B}_{16} = 1011_2$
• $\text{C}_{16} = 1100_2$
• $\text{A}_{16} = 1010_2$
• $\text{9}_{16} = 1001_2$

Combining these, we get the $16\text{-bit}$ binary representation of $X$: $$X = 1011\,1100\,1010\,1001_2$$

Step 2: Convert Binary to Octal
Group the binary digits in sets of three, starting from the right (least significant bit). We pad with leading zeros on the left to complete the leftmost group:

Converting each $3\text{-bit}$ group to its decimal equivalent gives the octal representation: $$X = 136251_8$$

Therefore, the correct option is D.