GATE CS 2018 - Digital Logic Quiz-6 ( Boolean Algebra & Minimization-2)

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Question 1

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

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

• AA-2, B-3, C-4
• BA-1, B-2, C-3
• CA-1, B-3, C-4
• D2, B-4, C-3

Question 2

In the figure, as long as X₁=1 and X₂=1, the output Q remains

• Aat 1
• Bat 0
• Cat its initial value
• Dunstable

Question 3

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

• A2
• B3
• C4
• D5

Question 4

The output Y in the circuit below is always ‘1’ when

• Atwo or more of the inputs P,Q,R are ‘0’.
• Btwo or more of the inputs P,Q,R are ‘1’.
• Cany odd number of the inputs P,Q,R is ‘0’
• Dany odd number of the inputs P,Q,R is ‘1’.

Question 5

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=^∑ (4, 5, 6)
(S2)F=^∑ (0, 1, 2, 3, 7)
(S3)F=^{∏ (}4, 5, 6⁾
(S4)F=^{∏ (}0, 1, 2, 3, 7⁾
Which of the following is true?

• A(S1)-False, (S2)-True, (S3)-True, (S4)-False
• B(S1)-True, (S2)-False, (S3)-False, (S4)-True
• C(S1)-False, (S2)-False, (S3)-True, (S4)-True
• D(S1)-True, (S2)-True, (S3)-False, (S4)- False

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