Modified Hamming Codes in Computing Devices Technical Diagnostic Systems

Abstract

Previously unknown error detection characteristics by types and multiplicities in modified Hamming codes code words are established. The rules for constructing this modification of Hamming codes are described. Detailed characteristic tables of codes with data vectors lengths m = 4...16 are given. The considered code's error detection properties brief analysis is given. The results obtained in the study can be effectively used in the digital computing devices with controllable structures synthesis, as well as in the self-checking concurrent error-detection (CED) circuit synthesis using the Boolean complement method. The modified Hamming codes key property is the impossibility of 100 % double error detection in all code word bits when any single and double errors that occur only in data bits are detected. That is why it is recommended, when synthesizing a CED circuit using the Boolean complement method, to convert only those functions that describe the operating functions of the diagnostic object that will form the modified Hamming code control bits, and to separate the converted and non-convertible outputs into two groups of independent outputs. The experiment results with test combinational circuits presented in the article confirm the effectiveness of their use in the CED circuit synthesis by the Boolean complement method.