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A new class of circuits called "partially self-checking circuits" is described. These circuits have one mode of operation called secure mode in which every fault is tested in normal operation and no fault can cause an undetected error. They also have an insecure mode of operation in which undetected errors can occur; however, every fault that can cause an error in insecure mode is tested by some input in secure mode. One application of these circuits is in the arithmetic and logic unit (ALU) of a computer with data encoded in an error-detecting code. While there is no code simpler than duplication which detects single errors in logical operations such as AND and OR, it is shown that there exist partially self-checking networks to perform these operations. A commercially available medium-scale integration (MSI) chip, the 74181 4-bit ALU, can be used in a partially self-checking network to perform arithmetic and logical operations.