A method is proposed that is based on the partitioning of the input code variables into two sections, each section representing the binary form of a number Z/sub 1/ and Z/sub 2/, respectively. For a code with check base A=2/sup m/-1, two m-bit end-around carry adder trees calculate the modulo m residue of Z/sub 1/ and Z/sub 2/, while a totally self-checking (TSC) translator maps the output of the pair of trees onto m-variable two-rail code. A TSC two-rail checker maps the m-variable two-rail code onto one-out-of-two code. The checkers present significant improvement in the implementation cost, number of gate levels, and reliability over TSC checkers previously proposed in the literature.>

In this paper we give methods for the construction of systematic t-random error correcting and all unidirectional error detecting codes. Also we give the encoding/decoding algorithms and discuss their implementation.

The paper presents systematic procedures for decomposing a sequential machine into submachines some or all of which are realized by polylinear sequential circuits. This polylinear decomposition is based upon classes of subsets of the set of states which possess the substitution property rather than upon partitions with substitution property. These classes are easily found using the backward state transition function of the machine and enables one to treat uniformly and simultaneously the problems of state minimization, machine decomposition in the classical or the polylinear way, finding the lattice of the partitions with substitution property, and periodic decomposition based upon classes that correspond to cyclic partitions. Procedures are developed for deriving optimal all polylinear decompositions and "good" partial polylinear decompositions of a machine.

This correspondence presents a new unified approach for defining and finding the various types of partition pairs ("d", "t","r","j") of a sequential machine. The notion of separation (distinguishability) of states is the key factor of the new approach. By this and the notion of transition sets one can easily find all maximal partitions τ which are in "d","t","r", and "j" relation with a given partition ρ.