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

,Solution Manual to

Aritificial Neural Networks

(B. Yegnanarayana, Prentice Hall of India Pvt Ltd, New Delhi, 1999)




B. Yegnanarayana and S. Ramesh
Dept. of Computer Science and Engineering
Indian Institute of Technology Madras
Chennai - 600036


March 2001

, CHAPTER 1

Solution to problem 1 (a):

a1 -1

a2 -1
θ=0 s
+1
a3
Using the logic function,

f (x) = 1, x > θ

= 0, x ≤ θ
X
where x = wi ai , the truth table is obtained by giving all possible combinations of a 1 , a2 , a3 . The
i
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.

a1 a2 a3
00 01 11 10
0 0 1 0 0
1 0 0 0 0
Logic function s(a1 , a2 , a3 ) = ā1 ā2 a3



1

, (b)
a1 +1
θ=1
-1
θ=0 s
+1
a2 +1
a3


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:

a1 a2 a3
00 01 11 10
0 0 1 1 0
1 0 1 0 0
Logic function s(a1 , a2 , a3 ) = ā2 a3 + ā1 a3


(c)

+1
-1
a +1
θ=0 θ=−1 s
-1




Truth table:
a s(t − 1) s(t)

0 0 1
0 1 1
1 0 0
1 1 1

2