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In this paper, we present efficient self-checking implementations valid for all existing adder and arithmetic and logic unit (ALU) schemes (e.g., ripple carry, carry lookahead, skip carry schemes). Among all the known self-checking adder and ALU designs, the parity prediction scheme has the advantage that it requires the minimum hardware overhead for the adder/ALU and the minimum hardware overhead for the other data-path blocks. It also has the advantage to be compatible with memory systems checked by parity codes. The drawback of this scheme is that it is not fault secure for single faults. The scheme proposed in this work has all the advantages of the parity prediction scheme. In addition, the new scheme is totally self-checking for single faults. Thus, the new scheme is substantially better than any other known solution.