Assuming all numbers are in 2's complement representation, which of the…

2003

Assuming all numbers are in 2's complement representation, which of the following numbers is divisible by 11111011?

Answer: A. 11100111Key idea: Interpret 8-bit patterns as two's complement signed integers. The divisor 11111011 is -5, so check which candidate values are multiples of 5.…

  1. A.

    11100111

  2. B.

    11100100

  3. C.

    11010111

  4. D.

    11011011

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Correct answer: A

Key idea: Interpret 8-bit patterns as two's complement signed integers. The divisor 11111011 is -5, so check which candidate values are multiples of 5.

  • 11100111 → invert: 00011000; add 1 → 00011001 = 25, so value = -25. -25 ÷ -5 = 5 → divisible.

  • 11100100 → invert: 00011011; add 1 → 00011100 = 28, so value = -28. -28 ÷ -5 is not an integer → not divisible.

  • 11010111 → invert: 00101000; add 1 → 00101001 = 41, so value = -41. -41 ÷ -5 is not an integer → not divisible.

  • 11011011 → invert: 00100100; add 1 → 00100101 = 37, so value = -37. -37 ÷ -5 is not an integer → not divisible.

Conclusion: 11100111 (which represents -25) is the only number divisible by 11111011 (which represents -5).

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