# Digital Logic - Logic functions & Minimization

16:

Which of the following logic expression is incorrect?

 A. 1 ⊕ 0 = 1 B. 1 ⊕ 1 ⊕ 0 =1 C. 1 ⊕ 1 ⊕ 1 = 1 D. 1 ⊕ 1 = 0 Option: B Explanation :
17:

In the following Karnaugh map, corresponding switching function in its minimal form is

 A. F( w , x , y , z ) = x' z' B. F( w , x , y , z ) = ( x' + z' ) ( w + z' )( x + y+ z ) C. F( w , x , y , z ) = x z  + w' z + x' y' z' D. F( w, x , y , z ) = x' z' + w z' w z' + xyz Option: D Explanation :
18:

The minimum Boolean expression for the circuit is

 A. $\tiny \dpi{150} AB+AC+BC$ B. $\tiny \dpi{150} A+BC$ C. $\tiny \dpi{150} A+B$ D. $\tiny \dpi{150} A+B+C$ Option: A Explanation : $\tiny \dpi{150} y=A(B+C)+AB+(A+B)C$     $\tiny \dpi{150} =AB+AC+AB+AC+BC$     $\tiny \dpi{150} =AB+AC+BC$
19:

Consider a function that is defined by the following truth table:

 A B C F(A, B, C ) 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 1 1 X 1 1 1 X

Which of the following statements about the minimal sum of products and minimal product of sums implementations is incorrect?

note that x represents don't care term

 A. They are logically equivalent because the don't cares are used in the same way B. They are not logically equivalent because the don't cares are used in the different ways C. They are not logically equivalent by definition D. They are logically equivalent by definition Option: A Explanation :
20:

What is the Boolean expression for the circuit given below ?

 A. F( A , B ) = A' B + A' B' = A' B. F( A , B ) = A ⊕ B C. F( A , B ) = A' + B' D. F( A , B ) = A' B' Option: A Explanation :