Boolean Algebra PYQ QUIZ GATE CS

The truth table


represents the Boolean function

The simplified SOP (Sum Of Product) form of the boolean expression (P + Q' + R') . (P + Q' + R) . (P + Q + R') is

The Boolean function x'y' + xy + x'y is equivalent to

Let ⊕ and ⊙ denote the Exclusive OR and Exclusive NOR operations, respectively. Which one of the following is NOT CORRECT?

Let, x1⊕x2⊕x3⊕x4 = 0 where x1, x2, x3, x4 are Boolean variables, and ⊕ is the XOR operator. Which one of the following must always be TRUE ?

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?

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

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?

Consider the minterm list form of a Boolean function F given below.

F(P, Q, R, S) = Σm(0, 2, 5, 7, 9, 11) + d(3, 8, 10, 12, 14) 

Here, m denotes a minterm and d denotes a don't care term. The number of essential prime implicants of the function F is ______ .

Note:

This was Numerical Type question.

If P, Q, R are Boolean variables, then (P + Q')(PQ' + PR)(P'R' + Q') simplifies