GATE CS 2009 Q5 — Number Representations (Fixed and Floating Point)

To find the equivalent value of the octal number $(1217)_8$, we can convert it to binary first, and then group the bits to find its hexadecimal representation.

Step 1: Convert Octal to Binary

Each octal digit corresponds to a $3$-bit binary number:

• $1 \rightarrow 001$
• $2 \rightarrow 010$
• $1 \rightarrow 001$
• $7 \rightarrow 111$

Combining these, we get:

$$(1217)_8 = (001\ 010\ 001\ 111)_2$$

Step 2: Convert Binary to Hexadecimal

Group the binary digits into groups of $4$ starting from the right (least significant bit):

$$\underbrace{0010}_{2} \quad \underbrace{1000}_{8} \quad \underbrace{1111}_{\text{F}}$$

Thus, the hexadecimal representation is $(28\text{F})_{16}$, which can be written with a leading zero as $(028\text{F})_{16}$.

Therefore, the correct option is B.