What shall be the 2’s complement representation of -24 in a 16-bit computer?

2018

What shall be the 2’s complement representation of -24 in a 16-bit computer?

  1. A.

    1111 1111 1110 1001

  2. B.

    1111 1111 1110 1001

  3. C.

    1111 1111 1110 0111

  4. D.

    1111 1111 1110 1000

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Correct answer: D

Key idea: Two's complement of a negative integer is formed by taking the 1's complement (flip all bits) of its positive binary form and then adding 1. For positive integers, the two's complement representation is the same as the ordinary binary representation with leading zeros. Step 1: Write +24 in 16-bit binary: 24₁₀ = 0000 0000 0001 1000 If the question asks for +24, the 16-bit two's complement representation is: 0000 0000 0001 1000 If the question intends the representation of -24, compute the 1's complement and then add 1: 1's complement (flip bits of 0000 0000 0001 1000): 1111 1111 1110 0111

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