71. The Boolean functions can be expressed in canonical SOP (sum of products) and POS (product of sums) form. For the functions, Y = A + BC, which are such two forms—
    

1. 1. Y = Σ (1, 2, 6, 7) and Y = Π (0, 2, 4)
      

   
   
   

   2. Y = Σ (1, 4, 5, 6, 7) and Y = Π (0, 2, 3)
      

   
   
   

   3. Y = Σ (1, 2, 5, 6, 7) and Y = Π (0, 1, 3)
      

   
   
   

   4. Y = Σ (1, 2, 4, 5, 6, 7) and Y= Π (0, 2, 3, 4)

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given Y = A + BC
   From K-map
   Y = Σ m (1, 4, 5, 6, 7)
   and
   Y = Π (0, 2, 3)

   
   

   Correct Option: B

   Given Y = A + BC
   From K-map
   Y = Σ m (1, 4, 5, 6, 7)
   and
   Y = Π (0, 2, 3)

   
   

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72. Consider the following statements:
    1. Minimization using Karnaugh map may not provide unique solution.
    2. Redundant grouping in Karnaugh map may result in non-minimized solution.
    3. Don't care states of used in Karnaugh map for minimization, the minimal solution is not obtained.
    Which of the statements given above are correct?
    

1. 1. 1, 2 and 3
      

   
   
   

   2. 2 and 3 only
      

   
   
   

   3. 1 and 3 only
      

   
   
   

   4. 1 and 2 only

   
   
   

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1. View Hint View Answer Discuss in Forum

   With reference to K-map
   ● Minimization using Karnaugh map may not provide unique solution
   ● Redundant grouping in Karnaugh map may result in non-minimized solution.

   Correct Option: D

   With reference to K-map
   ● Minimization using Karnaugh map may not provide unique solution
   ● Redundant grouping in Karnaugh map may result in non-minimized solution.

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73. The black box in the figure consists of a minimum complexity circuit that uses only AND, OR and NOT gates. The function f(x, y, z) = 1 whenever x, y are different and 0 otherwise. In addition the 3 inputs x, y, z are never all the same value. Which one of the following equations leads to the correct design for the minimum complexity circuit?
    
    
    
    

1. 1. x' y + xy'
      

   
   
   

   2. x + y'z
      

   
   
   

   3. x'y'z' + xy'z
      

   
   
   

   4. xy + y'z + z'

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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74. What is the Boolean expression for the truth table shown below?
    
    
    

1. 1. B (A + C) (A + C)

   
   
   

   2. B (A +C) ( A+ C)

   
   
   

   3. B( A + B (A + C) (A + C)

   
   
   

   4. B (A + C) (A + + C)

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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75. A full-adder can be made out of—
    

1. 1. Two half-adders
      

   
   
   

   2. Two half-adders and a NOT gate
      

   
   
   

   3. Two half-adders and an OR gate
      

   
   
   

   4. Two half-adders and an AND gate

   
   
   

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1. View Hint View Answer Discuss in Forum

   A full-adder can be made out of a two half-adders and an OR gate.
   

   Correct Option: C

   A full-adder can be made out of a two half-adders and an OR gate.
   

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