The minimal test set for sorting networks and the use of sorting networks in self-testing checkers for unordered codes

It is shown that an n-input sorting network (SN) can be used to implement all n-variable symmetric threshold functions, using the least amount of hardware. A procedure of generating the minimal test set for K.E. Batcher's SNs is presented. An upper bound is determined for the number of tests required to detect all stuck-at faults in an n-input SN; it is fewer than in similar designs used to date. Finally, it is shown that the SNs can be used to realize easily testable self-testing checkers (STCs) for m-out-of-2m codes and all J.M. Berger codes. The new STCs for m/2m codes (m>3) have the lowest gate count and require the fewest number of tests. Upper bounds are also found for the number of tests required by the new STCs for Berger codes with I information bits. For I>or=14 they require fewer gates than similar designs known to date.<>