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Carry-select adders are one of the faster types of adders. This paper proposes a scheme that encodes the sum bits using two-rail codes; the encoded sum bits are then checked by self-checking checkers. The multiplexers used in the adder are also totally self-checking. The scheme is illustrated with the implementation of a 2-bit carry select adder that can detect all single stuck-at faults on-line; the detection of double faults is not guaranteed. Adders of arbitrary size can be constructed by cascading the appropriate number of such 2-bit adders. A range of adders from 4 to 128 bits is designed using this approach employing a 0.5-mum CMOS technology. The transistor overhead in implementing these self-checking adders varies from 19.51% to 20.94%, and the area overhead varies from 16.07% to 20.67% compared to adders without built-in self-checking capability.