Whenever I see lists of interview questions it seems like bitwise operations are on there. I've never used these at work and I don't even remember needing to do it in school. I wanted to see if I could answer a few of these. After a quick review of what each operation does this is what I came up with.
The first three methods--nthBitSet, countBits, and isPalindrome--are fairly intuitive and I feel like they could be reasonable interview questions.
For adding and multiplying I cheated and looked up the algorithms. They sort of make sense, like the repeated additions for multiplication, but it would have taken a long time to come up with that on my own.