Digital Logic Design GATE CS and IT previous year questions with Answer

Ques 1 Gate 2024 Set-2

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A processor uses a 32-bit instruction format and supports byte-addressable memory access. The ISA of the processor has 150 distinct instructions. The instructions are equally divided into two types, namely R-type and I-type, whose formats are shown below.
R-type Instruction Format:

In the OPCODE, 1 bit is used to distinguish between I-type and R-type instructions and the remaining bits indicate the operation. The processor has 50 architectural registers, and all register fields in the instructions are of equal size.
Let 𝑋 be the number of bits used to encode the UNUSED field, 𝑌 be the number of bits used to encode the OPCODE field, and 𝑍 be the number of bits used to encode the immediate value/address field. The value of 𝑋 + 2𝑌 + 𝑍 is ________

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Ques 2 Gate 2024 Set-2

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Consider 4-variable functions f1, f2, f3, f4 expressed in sum-of-minterms form as given below.
f1 = ∑(0,2,3,5,7,8,11,13)
f2 = ∑(1,3,5,7,11,13,15)
f3 = ∑(0,1,4,11)
f4 = ∑(0,2,6,13)

With respect to the circuit given above, which of the following options is/are CORRECT?

A

Y =∑(0,1,2,11,13)

B

Y =Π(3,4,5,6,7,8,9,10,12,14,15)

C

Y =∑(0,1,2,3,4,5,6,7)

D

Y =Π(8,9,10,11,12,13,14,15)

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Ques 3 Gate 2024 Set-2

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Consider the following expression: 𝑥[𝑖]=(𝑝+𝑟)∗−𝑠[𝑖]+𝑢/𝑤. The following sequence shows the list of triples representing the given expression, with entries missing for triples (1), (3), and (6).

Which one of the following options fills in the missing entries CORRECTLY?

A

(1) =[]⁡⁡𝑠⁡⁡𝑖   (3) * (0) (2)   (6) []=⁡⁡𝑥⁡⁡𝑖

B

(1) []=⁡⁡𝑠⁡⁡𝑖   (3) –⁡(0)⁡(2)   (6) =[] ⁡𝑥⁡⁡(5)

C

(1) =[] ⁡𝑠⁡𝑖   (3) * (0)⁡⁡(2)   (6) []= ⁡𝑥⁡⁡(5)

D

(1) []= ⁡𝑠⁡⁡𝑖   (3) –⁡(0)⁡(2)   (6) =[] 𝑥⁡⁡𝑖

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Ques 4 Gate 2024 Set-2

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Consider an array X that contains n positive integers. A subarray of X is defined to be a sequence of array locations with consecutive indices. The C code snippet given below has been written to compute the length of the longest subarray of X that contains at most two distinct integers. The code has two missing expressions labelled (𝑃)⁡and (𝑄).

Which one of the following options gives the CORRECT missing expressions?
(Hint: At the end of the i-th iteration, the value of len1 is the length of the longest subarray ending with X[i] that contains all equal values, and len2 is the length of the longest subarray ending with X[i] that contains at most two distinct values.)

A

𝑃) len1+1     (𝑃) 1

B

(𝑃) 1             (𝑃) len2+1

C

(𝑄) len2+1   (𝑄) len1+1

D

(𝑄) len2+1   (𝑄) len1+1

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Ques 5 Gate 2022

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Consider a digital display system (DDS) shown in the figure that displays the contents of register X. A 16-bit code word is used to load a word in X, either from S or from R. S is a 1024-word memory segment and R is a 32-word register file. Based on the value of mode bit M, T selects an input word to load in X. P and Q interface with the corresponding bits in the code word to choose the addressed word. Which one of the following represents the functionality of P, Q, and T?

A

P is 10:1 multiplexer; Q is 5:1 multiplexer; T is 2:1 multiplexer

B

P is 10:2¹⁰ decoder; Q is 5:2⁵ decoder; T is 2:1 encoder

C

P is 10:2¹⁰ decoder; Q is 5:2⁵ decoder; T is 2:1 multiplexer

D

P is 1:10 de-multiplexer; Q is 1:5 de-multiplexer; T is 2:1 multiplexer

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Ques 6 Gate 2022

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The following simple undirected graph is referred to as the Peterson graph

Which of the following statements is/are TRUE?

A

The chromatic number of the graph is 3.

B

The graph has a Hamiltonian path.

C

The following graph is isomorphic to the Peterson graph.

D

The size of the largest independent set of the given graph is 3. (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)

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Ques 7 Gate 2022

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Let R1 and R2 be two 4-bit registers that store numbers in 2’s complement form. For the operation R1+R2, which one of the following values of R1 and R2 gives an arithmetic overflow?

A

R1 = 1011 and R2 = 1110

B

R1 = 1100 and R2 = 1010

C

R1 = 0011 and R2 = 0100

D

R1 = 1001 and  R2 = 1111

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Ques 8 GATE 2021 SET-1

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Consider a 3-bit counter, designed using T flip-flops, as shown below:

Assuming the initial state of the counter given by PQR as 000, what are the next three states?

A

011, 101, 000

B

001, 010, 111

C

011, 101, 111

D

001, 010, 000

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Ques 9 GATE 2021 SET-1

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Consider the following Boolean expression.
F = (X + Y + Z)(X̅ + Y)(Y̅ + Z)
Which of the following Boolean expressions is/are equivalent to F̅ (complement of F)?

A

(X̅ + Y̅ + Z̅)(X + Y̅)(Y + Z̅)

B

XY̅ + Z̅

C

(X + Z̅)(Y̅ + Z̅)

D

XY̅ + YZ̅ + X̅Y̅Z̅

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Ques 10 GATE 2021 SET-1

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Consider the following Boolean expression.
F = (X + Y + Z)(X̅ + Y)(Y̅ + Z)
Which of the following Boolean expressions is/are equivalent to F̅ (complement of F)?

A

(X̅ + Y̅ + Z̅)(X + Y̅)(Y + Z̅)

B

XY̅ + Z̅

C

(X + Z̅)(Y̅ + Z̅)

D

XY̅ + YZ̅ + X̅Y̅Z̅

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