Hardware is irrelevant. The analysis is mathematical and abstract. The model that people typically work in when doing this analysis is the comparison model: one < comparison costs 1 (http://en.wikipedia.org/wiki/Comparison_sort). There are other models that more closely resemble computers. For example, in the cell probe model (http://www.itl.nist.gov/div897/sqg/dads/HTML/cellProbeModel....) you have a word size (e.g. 32 bits, but the exact number is irrelevant) and you can construct radix sort in that model.
If all values in your set of numbers to sort are unique, then quicksort is indeed O(n lg n) worst case if you pivot about the median. If there are duplicate values, can you think of a way to still guarantee worst case O(n lg n)?
If all values in your set of numbers to sort are unique, then quicksort is indeed O(n lg n) worst case if you pivot about the median. If there are duplicate values, can you think of a way to still guarantee worst case O(n lg n)?