  When algorithms for sorting and searching are applied to keys that are
represented as bit strings, we can quantify the performance of the algorithms
not only in terms of the number of key comparisons required by the algorithms
but also in terms of the number of bit comparisons. Some of the standard
sorting and searching algorithms have been analyzed with respect to key
comparisons but not with respect to bit comparisons. In this paper, we
investigate the expected number of bit comparisons required by Quickselect
(also known as Find). We develop exact and asymptotic formulae for the expected
number of bit comparisons required to find the smallest or largest key by
Quickselect and show that the expectation is asymptotically linear with respect
to the number of keys. Similar results are obtained for the average case. For
finding keys of arbitrary rank, we derive an exact formula for the expected
number of bit comparisons that (using rational arithmetic) requires only finite
summation (rather than such operations as numerical integration) and use it to
compute the expectation for each target rank.
