In 16-bit 2’s complement representation, the decimal number −28 is:

2019

In 16-bit 2’s complement representation, the decimal number −28 is:

Answer: C. 1111 1111 1110 0100 — Answer: 1111 1111 1110 0100 Steps: Write +28 in 16 bits: 0000 0000 0001 1100. Invert all bits (one's complement): 1111 1111 1110 0011. Add 1 to get two's…

  1. A.

    1111 1111 0001 1100

  2. B.

    0000 0000 1110 0100

  3. C.

    1111 1111 1110 0100

  4. D.

    1000 0000 1110 0100

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Correct answer: C

Answer: 1111 1111 1110 0100

Steps:

  • Write +28 in 16 bits: 0000 0000 0001 1100.

  • Invert all bits (one's complement): 1111 1111 1110 0011.

  • Add 1 to get two's complement: 1111 1111 1110 0100.

  • Verify by converting back: invert 1111 1111 1110 0100 -> 0000 0000 0001 1100, add 1 -> 0000 0000 0001 1100 = 28, confirming the negative representation is -28.

Note: The 8-bit two's complement for -28 is 1110 0100; sign-extending that to 16 bits gives the same result: 1111 1111 1110 0100.

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