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?
- A.
11100111
- B.
11100100
- C.
11010111
- 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).