The four input lines for the network in Fig. 15.15 provide the binary equivalents of the numbers 0, 1, 2,..., 15, where each number is represented as abce, with e the least significant bit.

(a) Find the d.n.f. of g, whose value is 1 exactly when abce is the binary equivalent of 1, 2, 4, or 8.
(b) Draw the two-level gating network for g as a minimal sum of products.
(c) If this network is part of a larger network and, consequently, the binary equivalents of the numbers 10 through 15 never occur as inputs, design a two-level gating network for g in this case.

Power detector e