Expected number of passes in a binary search scheme

The binary search scheme is a method of finding a particular file from a set of ordered files stored in a computer. This scheme involves examining the middle file, and eliminating those files which do not contain the required file. This procedure is repeated until the required file is found.

In this paper an exact expression for the expected number of passes required to find a file selected at random is derived. The expected number of passes is shown to be asymptotically equal to log₂ k where k is the number of files. The asymptotic approximate values are compared to the exact values.