GATE | Gate IT 2008 | Question 8
Consider the following Boolean function of four variables
f(A, B, C, D) = Σ(2, 3, 6, 7, 8, 9, 10, 11, 12, 13)
The function is
(A) independent of one variable
(B) independent of two variables
(C) independent of three variable
(D) dependent on all the variables
Answer: (A)
Explanation:
The Karnaugh map solutions of the given function can be obtained in two ways. These are the minimal functions that can be obtained. Thus the functions obtained are independent of variable “D”.
| A’B’ | A’B | AB | AB’ | ||
| 00 | 01 | 11 | 10 | ||
| A’B’ | 00 | 1 | 1 | ||
| A’B | 01 | 1 | 1 | ||
| AB | 11 | 1 | 1 | ||
| AB’ | 10 | 1 | 1 | 1 | 1 |
A’C+AC’+AB’
| A’B’ | A’B | AB | AB’ | ||
| 00 | 0 1 | 11 | 10 | ||
| A’B’ | 00 | 1 | 1 | ||
| A’B | 01 | 1 | 1 | ||
| AB | 11 | 1 | 1 | ||
| AB’ | 10 | 1 | 1 | 1 | 1 |
A’C+AC’+B’C
Related :
https://www.geeksforgeeks.org/introduction-of-k-map-karnaugh-map/
https://www.youtube.com/watch?v=ygm25sqqepg&spfreload=10
https://www.youtube.com/watch?v=i_HYxdri69Y
This solution is contributed by Kriti Kushwaha.
Quiz of this Question
Attention reader! Don’t stop learning now. Practice GATE exam well before the actual exam with the subject-wise and overall quizzes available in GATE Test Series Course.
Learn all GATE CS concepts with Free Live Classes on our youtube channel.
