Regular structures and testing: RCC-adders

Abstract

We confine ourselves to one of the basic problems of testing, the test pattern generation problem for combinational circuits, and study the relation between structural properties and test complexity.

Here, this relation is looked at in detail for Recursive Carry Computation adders. The class of RCC-adders has been introduced in [BeKo] and contains a wide range of different adder realizations (e.g., optimal time adders such as the carry look-ahead adder of [BrKu] and the conditional carry adder of [BeKo]). We show that symbolic computation can be used to define this class and at the same time offers a uniform test approach which can be applied at an early stage of the design process. The class of RCC-adders itself splits into several subclasses which are specified by structural properties of the overall computation scheme and functional properties of the basic cells. Optimal complete test sets with respect to two commonly used fault models, the single stuck-at fault model and the single cellular fault model, are developed for these RCC-subclasses. The cardinality of the test sets depends on the choice of the fault model and on structural properties of the RCC-subclass.

To summarize our results, we finally obtain two tables with upper and lower bounds characterizing the test complexity of classes of RCC-adders. The upper bounds are obtained by the effective construction of complete test sets. The cardinality of these sets varies between a logarithmic or linear number of patterns for an n-bit RCC-adder.

This work was supported by DFG, SFB 124, TP B1, VLSI Entwurfsmethoden und Parallelität, and by BMFT Grant 413-5839-ITS8501A7, Kooperationsprojekt TESUS der Firmen Nixdorf und Siemens