GATE | GATE CS 2010 | Question 8

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

(A)

(C3D8)₁₆

(B)

(187B)₁₆

(C)

(F878)₁₆

(D)

(987B)₁₆

Answer: (A)

Explanation:

Explanation:

P = (F87B)₁₆ is -1111 1000 0111 1011 in binary

Note that most significant bit in the binary representation is 1, which implies that the number is negative. To get the value of the number performs the 2’s complement of the number. We get P as -1925 and 8P as -15400 

Since 8P is also negative, we need to find 2’s complement of it (-15400) 
Binary of 15400 = 0011 1100 0010 1000 
2\’s Complement = 1100 0011 1101 1000 = (C3D8)₁₆

Explanation 2 : (Easy way):

P = (F87B)₁₆ is (1111 1000 0111 1011)₂ in binary 

Note that the most significant bit in the binary representation is 1, which implies that the number is negative. To get the value of the number, the 2’s complement of the number is performed. We get P as -1925

The binary of (1925)₁₀ is (0000 0111 1000 0101)₂

Now 8P= left shift P 3 times = (0011 1100 0010 1000)₂   for a negative sign it is  (1011 1100 0010 1000)₂

2’s Complement = 1100 0011 1101 1000 = (C3D8)₁₆

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