On the number of locations required in the content-addressable memory implementation of multiple-varied functions

A multiple-valued function can be realized by a binary content addressable memory (CAM), a decoder which converts multiple-valued inputs to binary addresses, and a decoder which converts the binary CAM outputs to a multiple-valued output. Of particular interests is the number of CAM locations required in a specific implementation. In this paper, an upper bound on the storage requirements is derived for m-valued n-input functions. This is compared with the storage requirements for specific functions, such as the MIN and MAX functions. Also, the average number of locations is computed for m-valued n-input functions and is shown to be somewhat more than one-half of the upper bound.