**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**

**Answer: D**

**check video lecture on LOGIC GATES**

**Explanation:**

**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 given 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˅↔**

**Answer: B**

Explanation:

**Answer: D**

**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) ¼**

**Answer: B**

**Explanation:**

**select 10 bits and with every bit we have two choice either 0 or 1 so the total no of 10 length bit strings are 2^10**

**now in palindrome if we chose first 5 bits then our job is done as next 5 are fixed ( first 5 in reverse order).**

**So, for five bits can be chosen in 25 (for every bit either 0 or 1).**

**Probability = 2^5/2^10= 1/ 32**

**Given the following graphs :**

**Which of the following is correct?**

**(A) G _{1} contains Euler circuit and G_{2} does not contain Euler circuit.**

**(B) G _{1} does not contain Euler circuit and G_{2} contains Euler circuit.**

**(C) Both G _{1} and G_{2} do not contain Euler circuit.**

**(D) Both G _{1} and G_{2} contain Euler circuit.**

**Answer: C**

**Explanation:**

**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}**

**Answer: C**

**Explanation:**

**(326.4) _{8 }= 8^{2 }x 3 + 8^{1} x 2 + 8^{0} x 6 . 8^{-1} x 4 = ( 214.5)_{10}**

**another way convert into decimal **

**To convert in hexa decimal i assume you already familiar with the conventional way there is also a shortcut which is only applicable if one base can be written in the power of another base eg.( r _{1})^{m }= r_{2} **

**(326.4) _{8 }= (011010110.100)_{2} here we expanded every digit in three bits**

3 |
2 |
6 |
. |
4 |

011 |
010 |
110 |
. |
100 |

**(011010110.100) _{2} = (D6.8)_{16 } here we grouped every 4 bits**

0000 |
1101 |
0110 |
. |
1000 |

0 |
D |
6 |
. |
8 |

**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**

**Answer: C**

**check video lecture on how to find sign magnitude,1’s compliment and 2’s compliment**

**The Karnaugh map for a Boolean function is given as:**

**The simplified Boolean equation for the above Karnaugh Map is**

**(A) AB + CD + AB’ + AD (B) AB + AC + AD + BCD**

**(C) AB + AD + BC + ACD (D) AB + AC + BC + BCD**

**Answer: B**

Explanation:

**Which of the following logic operations is performed by the following given combinational circuit ?**

**(A) EXCLUSIVE-OR (B) EXCLUSIVE-NOR**

**(C) NAND (D) NOR**

**Answer: A**

**Explanation:**

**(X+(X+Y)’)’ + (Y+(X+Y)’)’**

**Apply DE MORGAN theorem**

**X'(X+Y)+Y'(X+Y)**

**XX’+X’Y+Y’X+Y’Y**

**0+X’Y+Y’X+0**

**X XOR Y**

**Match the following:**

List – I |
List – II |

1. Controlled Inverter |
i. a circuit that can add 3 bits |

2. Full adder |
ii. a circuit that can add two binary numbers |

3. Half adder |
iii. a circuit that transmits a binary word or its 1’s complement |

4. Binary adder |
iv. a logic circuit that adds 2 bits |

**Codes :**

** a b c d**

**(A) iii ii iv i**

**(B) ii iv i iii**

**(C) iii iv i ii**

**(D) iii i iv ii**

**Answer: D**

**Explanation:**

**Half adder-> Its is used to add 2 bits.**

**Full adder-> It is used to add 3 bits.**

**controlled inverter-> a circuit that transmits a binary word or its 1’s complement**

**Binary adder -> It is used to add 2 binary numbers**