The four input lines for the gating network shown in Fig. 15.12 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) Determine the d.n.f. of f, whose value is 1 for abce prime, and 0 otherwise.
(b) Draw the two-level gating network for f as a minimal sum of products.
(c) We are informed that the given network is part of a larger network and that, as a result, the binary equivalents of the numbers 10 through 15 are never provided as input. Design a two-level gating network for f under these circumstances.

a Prime number detector