Generate the answer for a given question. The question requires common knowledge of English. Make sure that the answer is in detail, long, consistent with the context, and requires general knowledge of English. To be less repetitive, please vary your language for each question. Give a proper explanation to answer, and if necessary, provide the definition of various terms. And conclude your answer if it's long. If you have used other resources (e.g., Merriam Webster's.) to answer the question, include citations in your answer. You don't need to paraphrase the context of your resources, but make sure that your answer is consistent and complete.

Input: Consider Input: There is a concept in computer science which deals with how to demonstrate negative binary numbers. Two methods for achieving this goal are ones' complement and two's complement. Since I got acquainted with these methods, this question never stops coming to my mind that why the apostrophe is placed differently in ones' vs two's? I also saw many articles using one's instead. Even Google suggests that I might be mistaken! So I want to resolve this issue once and for all. Is it a stylistic preference? What causes this difference? And please provide more examples of similar usage.

Output: Donald Knuth, that doyen of computer science, says in Art of Computer Programming, Vol 2.: Detail-oriented readers and copy-editors should notice the position of the apostrophe in terms like 'two's complement' and 'ones' complement': a two's complement number is complemented with respect to a single power of 2, whereas a ones' complement number is complemented with respect to a long sequence of 1s. Indeed, there is also a twos' complement notation, which has radix 3 and complementation with respect to (2...22) (base 3).


Input: Consider Input: I want to use one word to express how people who have very different world views are naturally pushed apart, like water and oil. It's not quite repulsion, but it's the natural avoidance. Thoughts? Example below: I don't find them interesting and the feeling is mutual. So I'm happy for this natural [insert word here].

Output: Here, 'Repulsion' can be used. But it's a strong word. In simpler cases you can go with the words 'Aversion', 'Disinclination'. 'I don't find them interesting and the feeling is mutual. So I'm happy for this natural disinclination/aversion'


Input: Consider Input: The phrase to boil down to something can be found in most dictionaries. However, to me, it sounds colloquial to write Finding an exact solution to Eq. 1 boils down to ... A real-life example can be found here, and many more here. Interestingly, many of the examples are by non-native speakers. Is it good style to use this phrase in formal writing? (I am prepared to hear that if people use it, then it is OK.).


Output: As has been suggested in other answers, it is not very suitable in formal writing. Here are some alternatives you might consider: amount to be reduced to be a matter of be in essence