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 postfix 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 preorder (i.e. parentnode leftnode rightnode), we will drive it from ordered tree i.e. ↔ ~ ∧ p q ∨ ~ p ~q
And postorder(i.e. leftnode rightnode parentnode) 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  2A ∩ B A ∪ B = A + B  A ∩ BTherefore,
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. 2^{5} choices for first half and 2^{5} choices for second half.
Probability = favorable outcome / total outcome = 2^{5}/ 2^{10} = 1 / 2^{5} = 1 / 32.So, option (B) is correct.
Question 5 
Given the following graphs:
Which of the following is correct?
G_{1} contains Euler circuit and G_{2} does not contain Euler circuit.  
G_{1} does not contain Euler circuit and G_{2} contains Euler circuit.  
Both G_{1} and G_{2} do not contain Euler circuit.  
Both G_{1} and G_{2} 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} = 8^{2} * 3 + 8^{1} * 2 + 8^{0} * 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?
Signmagnitude  
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 endaround 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 Signmagnitude, 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:
By grouping we will simply get AB + AC + AD + BCD.
So, option (B) is correct.
Question 9 
Which of the following logic operations is performed by the following given combinational circuit?
EXCLUSIVEOR  
EXCLUSIVENOR  
NAND  
NOR 
Discuss it
Question 9 Explanation:
F is EXCLUSIVEOR between X and Y.
So, option (A) is correct.
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.