NIMCET 2015 — Computer PYQ

Step 1: Understand the Operation

Multiplying by $8$ is the same as multiplying by $2^3$.

In binary terms, this means performing a Left Shift by $3$ bits.

Step 2: Convert Hexadecimal to Binary

The hexadecimal value $(F87B{)}_{16}$ in $16$-bit binary is:

• $F\to 1111$

• $8\to 1000$

• $7\to 0111$

• $B\to 1011$

So, $P=1111100001111011$

Step 3: Perform Left Shift by 3 bits

Shifting the bits to the left by $3$ positions (and filling the right side with $0$s):

Original: $1111100001111011$

Shifted: $1100001111011000$

Step 4: Convert back to Hexadecimal

Now, group the shifted binary bits into sets of $4$ to find the hex value:

• $1100\to C$

• $0011\to 3$

• $1101\to D$

• $1000\to 8$

The resulting hexadecimal value is $(C3D8{)}_{16}$.

Conclusion:

The $2$'s complement representation of $8P$ is $(C3D8{)}_{16}$.

The correct option is (a).