The 16-bit 2’s complement representation of an integer is 1111 1111 1111 0101;…

2016

The 16-bit 2’s complement representation of an integer is 1111 1111 1111 0101; its decimal representation is _________.

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Correct answer: -11

Answer: -11

Explanation: The 16-bit two's complement number is 1111 1111 1111 0101.

  • Since the most significant bit is 1, the number is negative.

  • Find the magnitude by taking the two's complement: invert all bits to get 0000 0000 0000 1010 (which is 10 in decimal).

  • Add 1 to that result: 0000 0000 0000 1010 + 1 = 0000 0000 0000 1011 (which is 11 in decimal).

  • Therefore the decimal value is -11.

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