Exam (elaborations) TEST BANK FOR Artificial Neural Networks By B. Yegnanarayana (Instructors Solution Manual)

Solution to problem 1 (a): s -1 -1 q=0 +1 a1 a2 a3 Using the logic function, f(x) = 1; x  = 0; x   where x = X i wiai, the truth table is obtained by giving all possible combinations of a1; a2; a3. The results are shown in the following table. Truth table: a1 a2 a3 s 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 To derive the logic function, one can use the following Karnaugh map (K-map) representation of the truth table. The logic function is obtained from the map by expressing the terms corresponding to the entries with 1. 0 0 0 1 0 0 0 1 0 0 1 00 01 10 a2a3 11 a Logic function s(a1; a2; a3) = a1a2a3 1 (b) q=1 q=0 +1 -1 +1 +1 s a2 1 a3 a Truth table: a1 a2 a3 s 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 K-map representation of the truth table is as follows: 0 1 0 1 0 0 0 1 1 0 a1 a2a3 Logic function s(a1; a2; a3) = a2a3 + a1a3 (c) +1 q=0 q=-1 s -1 +1 a -1 Truth table: a s(t