This question was previously asked in

GATE CS 2010 Official Paper

Option 1 : (C3D8)_{16}

The correct answer is **option 1**

**Concept:**

When we multiply a number by 2 this means a binary representation of this number is shifted left

shifting depends upon how many time the number is multiplied by 2

**Explanation:**

Given a hexadecimal number in 2's complement and required in 2's complement

So, nothing want to change it

P = (F87B)16 = (1111 1000 0111 1011)_{2}

8P =2^{3}*P

23*P this means that the binary number that is represented by P is shifted 3 times left

So, it becomes

(1111 1000 0111 1011)2 = (1100 0011 1101 1000)_{2 }= **(C3D8) _{16}**

P = (F87B)16 = (1111 1000 0111 1011)2

Most significant bit is 1 here its mean number is negative

To get the value 2's complement of this is (0000 0111 1000 0101)_{2}

(0000 0111 1000 0101)2 =(-1925)_{10}

8P =8 × -1925 =-15400

now need to find 2's complement of -15400

(15400)_{10}= (0011 1100 0010 1000)2

take 2's complement of (0011 1100 0010 1000)2

(1100 0011 1101 1000)2 = (C3D8)16