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Two types of codes for checking logical operations digit by digit on two vectors of binary digits are studied. The first type attaches a check symbol to each vector of binary digits and requires that the check symbol for the logical function of two vectors can be determined from the check symbols of the two input vectors. The second type of coding is ordinary block coding into vectors of binary digits, with the added requirement that the coded vectors be processed digit by digit. The constraints on the codes resulting from the assumptions for the coding system are studied by typical algebraic arguments. It is shown that for both types of coding and for all nontrivial logical functions of two variables, except “exclusive or” and its complement, there is no system of checking simpler than duplication. For “exclusive or” and its complement, group alphabets can be used, and for the block coding these are the only codes which can be used.
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