UGC NET CS 2016 Aug – II
Question 1 |
The Boolean function [~(~p ∧ q) ∧ ~( ~p ∧ ~q)] ∨ (p ∧ r)] is equal to the Boolean function:
q | |
p ∧ r | |
p ∨ q | |
p
|
Discuss it
Question 1 Explanation:
We have Boolean function:
[~(~p ∧ q) ∧ ~( ~p ∧ ~q)] ∨ (p ∧ r)]
= [(p ∨ ~q) ∧ (p ∨ q ) ∨ (p ∧ r)]
= [p ∨ (p ∧ q) ∨ (p ∧ ~q) ∨(p ∧ r)]
= p[1 ∨ q ∨ ~q ∨ r]
= p
So, option (D) is correct.
Question 2 |
Let us assume that you construct ordered tree to represent the compound proposition (~ (p ∧ q)) ↔ (~ p ∨ ~ q). Then, the prefix expression and post-fix expression determined using this ordered tree are pgiven as ____ and _____ respectively.
↔~∧pq∨ ~ ~ pq, pq∧~p~q~∨↔ | |
↔~∧pq∨ ~ p~q, pq∧~p~q~∨↔ | |
↔~∧pq∨ ~ ~ pq, pq∧~p~~q∨↔ | |
↔~∧pq∨ ~ p~ q, pq∧~p~ ~q∨↔ |
Discuss it
Question 2 Explanation:
We have compound proposition (~ (p ∧ q)) ↔ (~ p ∨ ~ q):
Now we will construct ordered tree:
We are asked to determine pre-order (i.e. parent-node left-node right-node), we will drive it from ordered tree i.e. ↔ ~ ∧ p q ∨ ~ p ~q
And post-order(i.e. left-node right-node parent-node) from the ordered tree it is p q ∧ ~ p ~ q ~ ∨ ↔.
So, option (B) is correct.

Question 3 |
Let A and B be sets in a finite universal set U. Given the following: |A – B|, |A ⊕ B|, |A| + |B| and |A ∪ B| Which of the following is in order of increasing size ?
|A – B| < |A ⊕ B| < |A| + |B| < |A ∪ B| | |
|A ⊕ B| < |A – B| < |A ∪ B| < |A| + |B| | |
|A ⊕ B| < |A| + |B| < |A – B| < |A ∪ B| | |
|A – B| < |A ⊕ B| < |A ∪ B| < |A| + |B| |
Discuss it
Question 3 Explanation:
We will draw venn diagram for all set: |A – B|, |A ⊕ B|, |A| + |B| and |A ∪ B|
So, option (D) is correct.
Alternative way -

|A – B| = |A| - |A ∩ B| |A ⊕ B| = |A| + |B| - 2|A ∩ B| |A ∪ B| = |A| + |B| - |A ∩ B|Therefore,
|A – B| < |A ⊕ B| < |A ∪ B| < |A| + |B|
Question 4 |
What is the probability that a randomly selected bit string of length 10 is a palindrome?
1/64 | |
1/32 | |
1/8 | |
1/4 |
Discuss it
Question 4 Explanation:
In the given question we have a palindrome: in even length palindrome half length is fixed and rest is repeated. So, in 10 bit palindrome, we have 5 position to be filled with 2 choices each-
i.e. 25 choices for first half and 25 choices for second half.

Probability = favorable outcome / total outcome = 25/ 210 = 1 / 25 = 1 / 32.So, option (B) is correct.
Question 5 |
Given the following graphs:
Which of the following is correct?

G1 contains Euler circuit and G2 does not contain Euler circuit. | |
G1 does not contain Euler circuit and G2 contains Euler circuit. | |
Both G1 and G2 do not contain Euler circuit. | |
Both G1 and G2 contain Euler circuit. |
Discuss it
Question 5 Explanation:
Euler circuit does not contain odd length cycle.
Refer: Eulerian path and circuit for undirected graph
None of the above graph is Eulerian.
So, option (C) is correct.
Question 6 |
The octal number 326.4 is equivalent to
(214.2)10 and (D6.8))16 | |
(212.5)10 and (D6.8))16 | |
(214.5)10 and (D6.8))16 | |
(214.5)10 and (D6.4))16 |
Discuss it
Question 6 Explanation:
To solve this question we will apply traditional approach:
(326.4)8 = 82 * 3 + 81 * 2 + 80 * 6 . 8-1 * 4 = ( 214.5)10 is decimal representation.
For hexadecimal representation group binary sequence of (214.5) = (011010110.100)2 into group of 4.
i.e. 0 1101 0110. 1000 (0 can be padded after decimal) this is equivalent to- (D6.8)16.
So, option (C) is correct.
Question 7 |
Which of the following is the most efficient to perform arithmetic operations on the numbers?
Sign-magnitude | |
1’s complement | |
2’s complement | |
9’s complement |
Discuss it
Question 7 Explanation:
Sign's magnitude is only for sign convention (MSB is 1 then no is negative and if 0 then no is positive).
Main difference is that while adding numbers using 1′ s complement, we first do binary addition, then add in an end-around carry value. But, 2′ s complement has only one value for zero, and doesn’t require carry values.
9’s complement of a decimal number is the subtraction of it’s each digits from 9. Like 1’s complement, 9’s complement is used to subtract a number using addition.
2's complement representation is unambiguous for 0 (i.e., only positive 0), but Sign-magnitude, 1’s complement and 9’s complement are ambiguous representation for 0 (i.e., both positive and negative 0).
So, option (C) is correct.
Question 8 |
The Karnaugh map for a Boolean function is given as
The simplified Boolean equation for the above Karnaugh Map is

AB + CD + A`B + AD | |
AB + AC + AD + BCD | |
AB + AD + BC + ACD | |
AB + AC + BC + BCD |
Discuss it
Question 8 Explanation:

Question 9 |
Which of the following logic operations is performed by the following given combinational circuit?


EXCLUSIVE-OR | |
EXCLUSIVE-NOR | |
NAND | |
NOR |
Discuss it
Question 9 Explanation:

Question 10 |
Match the following:

(1) | |
(2) | |
(3) | |
(4) |
Discuss it
Question 10 Explanation:
Controlled Inverter is a circuit that transmits a binary word or its 1’s complement.
Full adder is a circuit that can add 3 bits.
Half adder is a logic circuit that adds 2 bits.
Binary adder is a circuit that can add two binary numbers.
So, option (D) is correct.
There are 50 questions to complete.