Self-Dual Digital Devices with Calculations Testing by Modified Hamming Code

The authors proposed to implement self-checking devices with built-in control circuits according by two diagnostic parameters – belonging of code words to modified Hamming codes and belonging of check functions to the type of self-dual Boolean functions. The principles of constructing modified Hamming codes are given. Conditions are established under which the check bits of modified Hamming codes will be described by self-dual Boolean functions. It is proved that for each value of the number of check bits k, there is only one value of the number of data bits m for which the check functions will be self-dual. It is m=2k–2, k ∈ ℕ (k>1). For all other modified Hamming codes, the check functions are not self-dual. A condition for converting check functions of such Hamming codes into self-dual functions is formulated. The authors proposed the structure of the organization of the built-in control circuit according by the two diagnostic parameters indicated above. The results of simulating self-dual devices with calculations testing using modified Hamming codes with self-dual control functions are presented.