Digital Logic GATE 2018 Solved Questions

Ques 1: Let βŠ• and βŠ™ denote the Exclusive OR and Exclusive NOR operations, respectively.

GATE 2018 Q no 4

Which one of the following is NOT CORRECT?

(A) (π‘ƒβŠ•Q)’= 𝑃 βŠ™ 𝑄

(B) 𝑃’ βŠ• 𝑄 = 𝑃 βŠ™ 𝑄

(C) 𝑃̅’βŠ• 𝑄’ = 𝑃 βŠ• 𝑄

(D) (𝑃 βŠ• 𝑃’) βŠ• 𝑄 = (𝑃 βŠ™ 𝑃’) βŠ™ 𝑄’

Ans: (D) (𝑃 βŠ• 𝑃’) βŠ• 𝑄 = (𝑃 βŠ™ 𝑃’) βŠ™ 𝑄’

Solution: (D) LHS= (𝑃 βŠ• 𝑃’) βŠ• 𝑄 = 1 βŠ• 𝑄 = Q’

(D) RHS = (𝑃 βŠ™ 𝑃’) βŠ™ 𝑄’ = 0 βŠ™ 𝑄’ = Q

Ques 2: Consider the sequential circuit shown in the figure, where both flip-flops used are positive edge-triggered D flip-flops.

GATE 2018 Q no 22

The number of states in the state transition diagram of this circuit that have a transition back to the same state on some value of β€œin” is _______.

Ans: 2


Here 00 on input 0 and 11 on input 1 have transition back to itself. So, answer is 2

Ques 3: Consider the unsigned 8-bit fixed point binary number representation below

GATE 2018 Q no 33

b7 b6 b5 b4 b3 . b2 b1 b0

where the position of the binary point is between b3 and b2. Assume b7 is the most significant bit.

Some of the decimal numbers listed below cannot be represented exactly in the above representation:

(i) 31.500

(ii) 0.875

(iii) 12.100

(iv) 3.001

Which one of the following statements is true?

(A) None of (i), (ii), (iii), (iv) can be exactly represented

(B) Only (ii) cannot be exactly represented

(C) Only (iii) and (iv) cannot be exactly represented

(D) Only (i) and (ii) cannot be exactly represented

Ans: (C) Only (iii) and (iv) cannot be exactly represented

Solution: 31.500 can be represented as 11111.100 in the above mentioned fixed form representation

0.875 can be represented as 00000.111

We can’t represent 3 and 4.

So, C is the correct answer.

Ques 4: Consider the minterm list form of a Boolean function 𝐹 given below.

GATE 2018 Q no 49

𝐹(𝑃,𝑄, 𝑅, 𝑆) = βˆ‘π‘š(0, 2, 5, 7, 9, 11) + 𝑑(3, 8, 10, 12, 14)

Here, π‘š denotes a minterm and 𝑑 denotes a don’t care term. The number of essential prime implicants of the function 𝐹 is _____

Ans: 3


Click here to read about implicants in detail

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