Special Aspects of Using Hamming Codes in the Synthesis of Self-Checking Digital Devices Based on the Data Inversion Method

In relation to the theory of synthesis of self-checking digital systems, synthesis Hamming codes are characterized by the following properties: their coders and decoders are described by self-dual and self-anti-dual Boolean functions. During the synthesis of an internal control scheme based on the specified diagnostic criteria, it is important to ensure the self-duality and self-anti-duality of the device. In this study, the task of constructing self-checking digital devices using time redundancy and the pulse mode of operation based on the data inversion method is considered. It is proposed to use as diagnostic features in the embedded control circuit (ECC) the membership of the generated functions in the self-dual and self-anti-dual Boolean functions classes, as well as the membership of the generated code word in a preselected Hamming code. It is established that the functions describing the check bits of Hamming codes can be either only self-dual, or only self-anti-dual, or partially self-dual and partially self-anti-dual. The values of the number of symbols in the codewords of Hamming codes for which the check symbols are described only by self-dual, or only self-anti-dual, or partially self-dual and partially self-anti-dual Boolean functions are established. Similar conditions are established for extended Hamming codes. The ECC of the organization’s structure according to several diagnostic criteria is given. It is noted that the structure can be based on any linear block code. However, for each specific code, conditions must be determined under which the check symbols will be described only by self-dual, or only by self-anti-dual, or by partially self-dual and partially self-anti-dual Boolean functions. It is found that the use of the properties of the Hamming codes makes it possible to synthesize in practice self-testing digital devices based on the data inversion method when checking calculations using several diagnostic criteria.