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Previous papers have shown that a ripple carry adder composed of several full adder cells can be completely tested by a minimum test set of size 8 independent of the number of cells in the ripple carry adder under single faulty cell assumption. The fault model assumed is that faults in a cell can change the cell behavior in any arbitrary way, as long as the cell remains a combinational circuit. In this paper, we assume that any number of cells can be faulty at any time. A minimum test set of size 11 which can detect arbitrary length ripple carry adders under this fault model is presented. For general (N, p) adders in which each cell is a p-bit adder, a minimum test set of size 3 × 22P − 1 is also presented.