Implementing Symmetric Functions with Hierarchical Modules for Stuck-At and Path-Delay Fault Testability

Abstract

A technique for implementing totally symmetric Boolean functions using hierarchical modules is presented. First, a simple cellular module is designed for synthesizing unate symmetric functions. The structure is universal, admits a recursive design, and uses only 2-input AND-OR gates. A universal test set of size (n2/8 + 3n/4) for detecting all single stuck-at faults can be easily determined for an n-input module, where n = 2k, k � 3. General symmetric functions are then realized following a unate decomposition method. The synthesis procedure guarantees full robust path-delay fault testability in the circuit. Experimental results on several symmetric functions reveal that the hardware cost of the proposed design is low, and the number of paths in the circuit is reduced significantly compared to those of earlier designs. Results on circuit area and delay for a few benchmark examples are also reported.