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GATE CS : Digital Logic Champion Quiz 1

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Question 1

Consider the following Boolean function of four variables:
f (w, x, y, z) =

(1,3,4,6,9,11,12,14)
The function is:

Question 2

Match the following Lists:
List-I (Logic)
A-

B-

C-

List-II (Function)
1- Sum
2- NAND
3- Carry
4- NOR

Question 3

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

Question 4

The truth table

represents the Boolean function

Question 5

If P, Q, R are Boolean variables, then

simplifies to

Question 6

The literal count of a boolean expression is the sum of the number of times each literal appears in the expression. For example, the literal count of (xy + xz’) is 4. What are the minimum possible literal counts of the product-of-sum and sum-of-product representations respectively of the function given by the following Karnaugh map ? Here, X denotes “don’t care”

Question 7

The simultaneous equations on the Boolean variables x, y, z and w,
x + y + z = 1
xy = 0
xz + w = 1

have the following Solution for x, y, z and w, respectively:

Question 8

Let ⊕denote the Exclusive OR (XOR) operation. Let ‘1’ and ‘0’ denote the binary constants. Consider the following Boolean expression for F over two variables P and Q:
F(P, Q) = ((1⊕P)⊕ (P⊕Q)) ⊕ ((P⊕Q)⊕ (Q⊕0))
The equivalent expression for F is

Question 9

The maximum number of Boolean expression that can be formed for the function f(x,y,z) satisfying the relation f(

) = f(x,y,z) is

Question 10

Let f(A,B) = A’ + B. Simplified expression for function f{f (x + y, y) , z} is

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GATE & PSU CS Digital Logic

Jun 25GATE & PSU CS