The Boolean function [~(~p ∧ q) ∧ ~( ~p ∧ ~q)] ∨ (p ∧ r)] is equal to the Boolean function:
p ∧ r
p ∨ q
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.
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∨↔
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.
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|
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|
What is the probability that a randomly selected bit string of length 10 is a palindrome?
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.
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.
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.
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
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.
Which of the following is the most efficient to perform arithmetic operations on the numbers?
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.
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
Question 8 Explanation:
By grouping we will simply get AB + AC + AD + BCD. So, option (B) is correct.
Which of the following logic operations is performed by the following given combinational circuit?
Question 9 Explanation:
F is EXCLUSIVE-OR between X and Y. So, option (A) is correct.
Match the following:
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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