Properties of arithmetic norms of integers are applied to the study of arithmetic BN modulo A codes. Some new properties of such codes are established. Bounds on the size of such codes are derived and an efflcient algorithm for finding the optimal single and double error-correcting BN modulo A codes is developed.

A tool employed in automated fault diagnosis is emphasized: path sensitization by partial Boolean difference analysis. Motivated by the analogy between a test system and a communication system, a model for fault detection of a logic net is outlined from the standpoint of information theory. The classical ``path sensitizing'' technique is made systematic using the partial Boolean difference. This technique is based on a new theorem on the partial Boolean difference. Finally, a programmable fault detection algorithm is presented along with an example.

This paper delineates an application of two classes of parity-check codes to the design for failure-tolerant counters. They are 1) a modified first-order Reed-Muller code and 2) the perfect Hamming code. The first code employs a majority element for implementing the error-correcting scheme while the second one makes use of a variable 2j-2+1-out-of-2j-1+1 majority element. These coding techniques can be applied in principle to other logic hardware to increase its reliability.

Properties of integers, related to the generation of the arithmetic AN codes, are investigated in this paper. A programmable algorithm for the computation of the binary norm of an arbitrary integer is developed. A table of norms of the natural numbers is generated and from this the distribution of integers of a given norm is found. These results are used to compute bounds on the size of ane-fold or less error-correcting AN code and to derive some further properties of single- and double-error-correcting AN codes.