Multiple choice

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

  1. 11100111

  2. 11100100

  3. 11010111

  4. 11011011
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A Correct answer
Explanation

We can't judge the no's in 2's complement first we need to convert them in decimal Given no. $ 11111011 \rightarrow 00000101 = 5 $
$ 11100111 \rightarrow 00011001 = 25 $ $ 11100100 \rightarrow 00011100 = 28 $
$ 11010111 \rightarrow 00101001 = 41 $ $ 11011011 \rightarrow 00100101 = 37 $

From all only option (1) is divisible by 5. Shortcut: To convert 2's complement no. directly into original binary, we should complement all the digits from MSB till the last one (1). Keep the last 1 from the LSB as it is. Observe the example.

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