If N is a 16-bit signed integer The 2’s complement representation of N is (F87B)<sub>16</sub>.The 2’s complement representation of 8*N is ________
Multiplying by 8 = \(2^3\) is an arithmetic left shift by 3 bits.
\(F87B_{16} = 1111\,1000\,0111\,1011\)
Shift left by 3 (drop the 3 leftmost bits, add three 0s on the right): \(1100\,0011\,1101\,1000 = C3D8_{16}\)
Check: \(N = F87B = -(0785_{16}) = -1925\). Then \(8N = -15400\), and \(-C3D8\) gives \(3C28_{16} = 15400\). Correct, and no overflow, since −15400 fits in 16 bits.
Answer: (A) \(C3D8_{16}\)
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