UGC NET CS 2016 Aug – II


Question 1
The Boolean function [~(~p ∧ q) ∧ ~( ~p ∧ ~q)] ∨ (p ∧ r)] is equal to the Boolean function:
A
q
B
p ∧ r
C
p ∨ q
D
p
Propositional and First Order Logic.    UGC NET CS 2016 Aug – II    
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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.
A
↔~∧pq∨ ~ ~ pq, pq∧~p~q~∨↔
B
↔~∧pq∨ ~ p~q, pq∧~p~q~∨↔
C
↔~∧pq∨ ~ ~ pq, pq∧~p~~q∨↔
D
↔~∧pq∨ ~ p~ q, pq∧~p~ ~q∨↔
Propositional and First Order Logic.    UGC NET CS 2016 Aug – II    
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Question 2 Explanation: 
We have compound proposition (~ (p ∧ q)) ↔ (~ p ∨ ~ q): Now we will construct ordered tree: 2 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
|A – B| < |A ⊕ B| < |A| + |B| < |A ∪ B|
B
|A ⊕ B| < |A – B| < |A ∪ B| < |A| + |B|
C
|A ⊕ B| < |A| + |B| < |A – B| < |A ∪ B|
D
|A – B| < |A ⊕ B| < |A ∪ B| < |A| + |B|
Propositional and First Order Logic.    UGC NET CS 2016 Aug – II    
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Question 3 Explanation: 
We will draw venn diagram for all set: |A – B|, |A ⊕ B|, |A| + |B| and |A ∪ B| 3 (2) 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?
A
1/64
B
1/32
C
1/8
D
1/4
Probability    UGC NET CS 2016 Aug – II    
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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- 333 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: 5 (1) Which of the following is correct?
A
G1 contains Euler circuit and G2 does not contain Euler circuit.
B
G1 does not contain Euler circuit and G2 contains Euler circuit.
C
Both G1 and G2 do not contain Euler circuit.
D
Both G1 and G2 contain Euler circuit.
Graph Theory    UGC NET CS 2016 Aug – II    
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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
A
(214.2)10 and (D6.8))16
B
(212.5)10 and (D6.8))16
C
(214.5)10 and (D6.8))16
D
(214.5)10 and (D6.4))16
Digital Logic & Number representation    Number Representation    UGC NET CS 2016 Aug – II    
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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?
A
Sign-magnitude
B
1’s complement
C
2’s complement
D
9’s complement
Digital Logic & Number representation    Number Representation    UGC NET CS 2016 Aug – II    
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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 8 (1) The simplified Boolean equation for the above Karnaugh Map is
A
AB + CD + A`B + AD
B
AB + AC + AD + BCD
C
AB + AD + BC + ACD
D
AB + AC + BC + BCD
Digital Logic & Number representation    UGC NET CS 2016 Aug – II    Logic functions and Minimization    
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Question 8 Explanation: 
8 (1) (1) 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? 111
A
EXCLUSIVE-OR
B
EXCLUSIVE-NOR
C
NAND
D
NOR
Digital Logic & Number representation    UGC NET CS 2016 Aug – II    Combinational Circuits    
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Question 9 Explanation: 
333333 F is EXCLUSIVE-OR between X and Y. So, option (A) is correct.
Question 10
Match the following: 10
A
(1)
B
(2)
C
(3)
D
(4)
Digital Logic & Number representation    UGC NET CS 2016 Aug – II    Combinational Circuits    
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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.


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