Logic functions and Minimization

Question 31

Given the following Karnaugh map, which one of the following represents the minimal Sum-Of-Products of the map?  

[caption width="800"] [/caption]

• xy + y\'z

• wx\'y\' + xy + xz

• w\'x + y\'z + xy

• xz + y

Question 32

The simultaneous equations on the Boolean variables x, y, z and w,

have the following solution for x, y, z and w, respectively.

• 0 1 0 0
• 1 1 0 1
• 1 0 1 1
• 1 0 0 0

Question 33

Which function does NOT implement the Karnaugh map given below?

• a
• b
• c
• d

Question 34

Consider the operations f(X, Y, Z) = X\'YZ + XY\' + Y\'Z\'  and  g(X, Y, Z) = X′YZ + X′YZ′ + XY Which one of the following is correct?

• Both {f} and {g} are functionally complete
• Only {f} is functionally complete
• Only {g} is functionally complete
• Neither {f} nor {g} is functionally complete

Question 35

The number of min-terms after minimizing the following Boolean expression is _________.

      [D′ + AB′ + A′C + AC′D + A′C′D]′

• 1
• 2
• 3
• 4

Question 36

The total number of prime implicants of the function f(w, x, y, z) = Σ(0, 2, 4, 5, 6, 10) is ________.

• 2

• 3

• 4

• 5

Question 37

Given the function F = P′ + QR, where F is a function in three Boolean variables P, Q and R and P′ = !P, consider the following statements.

  S1: F = Σ (4, 5, 6)
  S2: F = Σ (0, 1, 2, 3, 7)
  S3: F = Π (4, 5, 6)
  S4: F = Π (0, 1, 2, 3, 7) 

Which of the following is true?

• S1-False, S2-True, S3-True, S4-False
• S1-True, S2-False, S3-False, S4-True
• S1-False, S2-False, S3-True, S4-True
• S1-True, S2-True, S3-False, S4-False

Question 38

What is the minimum number of NAND gates required to implement a 2-input EXCLUSIVE-OR function without using any other logic gate?

• 3
• 4
• 5
• 6

Question 39

The function AB’C + A’BC + ABC’ + A’B’C + AB’C’ is equivalent to

• AC’+AB+A’C
• AB’+AC’+A’C
• A’B+AC’+AB’
• A’B+AC+AB’

Question 40

Which of the following expressions is equivalent to (A⊕B)⊕C

• (A+B+C)(A¯+B¯+C¯)
• (A+B+C)(A¯+B¯+C)
• ABC+A¯(B⊕C)+B¯(A⊕C)
• None