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It is noticed that the original disjoint subsets of each set appear in different groups. Hence, the three sets are steerable.Q.E.D. Based on the above lemmas we state the following theorem.Theorem 2: The sets of microcommands C, (i = 1, 2, · · ·, n) are steerable together if and only if the following conditions are satis fied:1) The sets are pairwise steerable.2) The disjoint subsets with distinct steering code of each set Q are the same when the set C, is steered with each of the remaining (« -1) sets.An example of three set steerability is shown in Fig. 7 for the sample microprogram. The disjoint groups are \(d Nop)(e Nop)(A)l and |(#)(i)(Nop)j. III. CONCLUSIONSWhen we obtain the minimum bit solution based on the formulation of Grasselli and Montanari [2], it may not turn out to be a good en gineering reduction as was pointed out by Agerwala [6]. We may then employ the technique of bit steering for further reduction in the bit dimension and obtain a good engineering solution. The concurrency matrix method presented in this paper is very useful in the detection of bit steerability and the encoding of two (or more) mutually ex clusive sets of microcommands. IV.Abstract-Bentley and Ottmann 1 present an algorithm for reporting all Κ intersections among Ν planar line segments in 0((7V + K) log N) time and 0(7V + A") storage. With a small modification that storage requirement can be re duced to 0(N) with no increase in computation time, which is important because Κ can grow as Θ(Ν 2 ).Index Terms-Computational geometry, geometric intersection problems, optimal algorithms, VLSI design rule checking.