A Note on Tributary Switching Networks

We read Miyata's recent paper' with inand 2) requires no greater appeal to in"commonly." I do not mean that my terest. We take issue only with his conclugenuity Indeed our derivation seems to remethod is anecessarily" superior to Cohn sion that his method is, except in special quire less ingenuity than Mivata's. and Lindamans method except in special cases, necesarilsueri s2 The fundamental theorem of majoritycases. cases, necessarily superior to our .= deiso loi,a ie nou aleae,i Eveni h aeo i zFoadFo-~Fl In developing combinational switching decision logic asgivenin ourearlierpaper, is there may be some case in Fwhich Cohn and theory, one may consider 1) the number of Lindaman's method may lead us to a better logic elements in any network and 2) the F(X, Y, Z, Q) result. But we do not know if it is always so fan-in of each element. The number of eleor how to get the result. In the meaning that ments per network is, of course, virtually = (X # Y #f -) # (X # Y if ) #fy (1) unlimited, whereas the fan-in of each is of some elements, I think my methods are usually severely restricted by physical conwhere menale I the cs oftF1sF and siderations. Nevertheless, orthodox writers on majority (threshold) logic tacitly make Ly F(X, X, Z, Q) Fu0 #F01. FUSACHIKA MIYATA the opposite assumptions. They take the eleResearch Lab. of Precision ments per network to be severely restricted fxya F(X, X, Z, Q), Machinery and Electronics (usually to one), but fan-in to be unlimited. Tokyo Inst. of Tech. They therefore tend to elaborate logic theory and X#Y#Z denotes a binary quantity that Ookayama, Meguro-ku Tokyo for physically impossible devices. Japan It is accordingly refreshing to find times written mX(Y +Z)+XYZ") Miyata attacking the real problem: synLike Miyata, we recognize that the first 3Received November 5, 1963. thesis of networks of components having term of I is just x.(y#z#u). Application of limited fan-in. Further, his method appears (1) to the second term yields to be both useful and novel. In comparing his method with ours, Mivata concludes that our method "depends mainly on special Ju= xy(0 + 0) 0 algebraic properties of the given logical function," and that his "method is better fuz XY( + u) = than the method of Cohn and Lindaman F(u except for certain special cases." Indeed, he .... z ) = (u i z # x y) # (i# z # xY) #0 A Note on Tributary Switching seems to prove that his method is necessarily = ( a z f x (" i z # x Networks better than ours for a broad class of functions specified by his condition (63b). The -(u 4 h4 ~) .(~ f~ ) In recent articles, K. K. Maitra1 and one example he gives of such a function isJ. Sklansky2 discuss methods of synthesis for "cascaded" or "tributary" switching netI = xIyzu + y(z + u)} + xcy(zi + fu). The last step above seems to be the only works composed of two-input gates (see