NIMCET 2021 — Computer PYQ

Step 1: Convert Octal to Binary

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

• $2⟹010$

• $2⟹010$

• $1⟹001$

• $7⟹111$

Combining them gives the complete binary string:

$$(2217{)}_8=(010010001111{)}_2$$

Step 2: Convert Binary to Hexadecimal

Group the binary digits into sets of 4 starting from the rightside (Least Significant Bit):

$$\underset{4}{\underbrace{0100}}\underset{8}{\underbrace{1000}}\underset{F}{\underbrace{1111}}$$

Now, convert each 4-bit group into its equivalent hexadecimal digit:

• $(0100{)}_2⟹4$

• $(1000{)}_2⟹8$

• $(1111{)}_2⟹15⟹F$

Putting them together, we get:

$$(48F{)}_{16}$$

Adding a leading zero to match the standard 4-digit format given in the options:

$$(048F{)}_{16}$$

Therefore, $(2217{)}_8$ is equivalent to $(048F{)}_{16}$.