P is a 16-bit signed integer. The 2’s complement representation of P is (F87B)₁₆ The 2’s complement representation of 8*P is

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 =2³*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