The Design of Complementary-Output Networks

Using the contact network as a representative of the class of combinational branch-type networks, various realization techniques are examined for their applicability or adaptability to the particular class of complementary-output networks, that is, two-output networks which have exactly one active output for each combination of the independent variables. Some elementary structural characteristics are developed and a particular class of functions which are minimally realized in separate parts is discussed. Upper and lower bounds are derived for the the number of contacts required to realize an arbitrary n-variable specification. Rudin's interconnection rules are extended to the non-series-parallel case and examples are given of their application. Trees are discussed in terms of a specific procedure proposed for their realization. Finally, Calingaert's reduction of the general multi-output problem to a single-output problem is reviewed in terms of the specific class of networks of interest here, and results, in conjunction with Moore's tables of minimal four-variable networks, in a table of minimal three-variable complementary-output networks.