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CSD · Most repeated questions

47 questions · 131 marks · 4 papers · 20 question types

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Computer System Design

Most repeated questions

Official Paper

Examination Instructions & Guidelines

Solve on notebook/paper first before checking solutions.
MCQ: Exactly 1 option is correct. Negative marking applies.
NAT: Numerical response. No negative marking.
Scientific calculator allowed for all calculations.
Official answer key is sealed at the end of this sheet.

Type 1 · asked 5 times · SOP/POS, K-maps & universal gates

Find the minimum number of 2-input NAND/NOR gates to implement a function

Q1NAT5 Marks·Write the number
Quiz 2 · 3 Aug 2025 (AN)Key ↓
Your answer:
Read the passage below, then answer Q2
Answer the given two subquestions based on the given minterm :
Q2NAT3 Marks·Write the number
Quiz 2 · 3 Aug 2025 (AN)Key ↓
If we want to implement the minimized expression using only 2-input NOR gates, what is the minimum number of NOR gates required, given inputs A, B, C, and D?
Your answer:
Q3NAT3 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:
Q4NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:
Q5NAT5 Marks·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
Answer the given question based on given timing diagram. Given that we only have 2-input NOR gates, what is the minimum number of NOR gates needed to represent a circuit with an output timing diagram same as Y?
Your answer:

Type 2 · asked 4 times · Multiplexers, decoders & delays

Find the minimum number of 2:1 multiplexers to implement a function

Read the passage below, then answer Q6
Answer the given two subquestions based on the given minterm :
Q6NAT3 Marks·Write the number
Quiz 2 · 3 Aug 2025 (AN)Key ↓
If we want to design the given minterm using 2:1 multiplexers, what is the minimum number of multiplexers required?
Your answer:
Q7NAT3 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:
Q8NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:
Q9NAT5 Marks·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
Your answer:

Type 3 · asked 3 times · Sequential circuits & counters

Trace a JK flip-flop circuit's output over the next few clock pulses

Q10NAT5 Marks·Write the number
Quiz 2 · 3 Aug 2025 (AN)Key ↓
Your answer:
Q11NAT3 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:
Q12NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 4 · asked 3 times · Logic gates & Boolean algebra

Find the probability a gate circuit outputs 1/0 for uniformly random inputs

Q13NAT3 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:
Q14NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:
Q15MCQ5 Marks·Choose one option
Quiz 1 · 26 Oct 2025 (AN)Key ↓
Consider the circuit shown below. Given that the inputs are supplied uniformly random,what is the probability of the output Y being at logic 0?
1. A0.75
2. B0.50
3. C0.33
4. D0.25
5. E1

Type 5 · asked 2 times · Number systems & binary arithmetic

True/false: one's complement of a 4-bit number

Q16MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
In a 4-bit system, the one’s complement of the binary number 1100 is 0111.
1. ATRUE
2. BFALSE
Q17MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
In a 4-bit system, the one’s complement of the binary number 1100 is 0011.
1. ATrue
2. BFalse

Type 6 · asked 2 times · Sequential circuits & counters

True/false: synchronous vs asynchronous counter clocking

Q18MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
A synchronous counter triggers all flipflops using a common clock signal, while an asynchronous counter triggers each flipflop using the output of the previous flipflop.
1. ATRUE
2. BFALSE
Q19MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
A synchronous counter triggers all flipflops using a common clock signal, while an asynchronous counter triggers each flipflop using the output of the previous flipflop.
1. ATrue
2. BFalse

Type 7 · asked 2 times · Latches & flip-flops

True/false: number of flip-flops needed for 64 states

Q20MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
In a system with 64 unique states, 4 flipflops are sufficient to represent all the states.
1. ATRUE
2. BFALSE
Q21MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
In a system with 64 unique states, 6 flipflops are sufficient to represent all the states.
1. ATrue
2. BFalse

Type 8 · asked 2 times · Multiplexers, decoders & delays

True/false: exactly one decoder output is high

Q22MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
In a decoder, at any point, exactly one of the outputs is 1 and all the rest are 0s.
1. ATRUE
2. BFALSE
Q23MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
In a decoder, at any point, exactly one of the outputs is 1 and all the rest are 0s.
1. ATrue
2. BFalse

Type 9 · asked 2 times · Number systems & binary arithmetic

True/false: transistor count growth under Moore's law

Q24MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
According to Moore’s law, if a computer system has 2 million transistors today, then it will have approximately 32 million transistors in 7 years.
1. ATRUE
2. BFALSE
Q25MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
According to Moore’s law, if a computer system has 2 million transistors today, then it will have approximately 32 million transistors in 8 years.
1. ATrue
2. BFalse

Type 10 · asked 2 times · Latches & flip-flops

Derive the D flip-flop input logic from a next-state truth table

Q26MCQ3 Marks·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
1. A
2. B
3. C
4. D
5. E
Q27MCQ3 Marks·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
1. A
2. B
3. C
4. D
5. E

Type 11 · asked 2 times · SOP/POS, K-maps & universal gates

Minimum gates for a 1-bit equality comparator using NOR/NAND only

Q28NAT3 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:
Q29NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 12 · asked 2 times · SOP/POS, K-maps & universal gates

Count minterms when output is 1 for exactly two of four inputs

Q30NAT3 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:
Q31NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 13 · asked 2 times · Sequential circuits & counters

Count reachable states of a D flip-flop circuit with an XNOR gate

Q32NAT3 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:
Q33NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 14 · asked 2 times · Sequential circuits & counters

State of a mod-12 up counter after 25 clock pulses

Q34NAT3 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Consider a mod-12 up counter with an initial state of 0111. What will be the state of the counter after 25 clock pulses?
Your answer:
Q35NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Consider a mod-12 up counter with an initial state of 0011. What will be the state of the counter after 25 clock pulses?
Your answer:

Type 15 · asked 2 times · Sequential circuits & counters

Number of unique states of an n-bit Johnson counter

Q36NAT3 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Consider a 10-bit Johnson counter. What is the total number of unique states it can cycle through?
Your answer:
Q37NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Consider a 9-bit Johnson counter. What is the total number of unique states it can cycle through?
Your answer:

Type 16 · asked 2 times · Bus, registers & instruction encoding

Write the hex control word for a register transfer on a common bus

Q38Short answer3 Marks·Write the answer
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:
Q39Short answer3 Marks·Write the answer
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 17 · asked 2 times · Bus, registers & instruction encoding

Minimum instruction bits for a 3-register ALU operation

Q40NAT3 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:
Q41NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 18 · asked 2 times · Bus, registers & instruction encoding

Maximum number of registers from a control word's register field

Q42NAT3 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:
Q43NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 19 · asked 2 times · Bus, registers & instruction encoding

Encode a MOV instruction into hexadecimal machine code

Q44Short answer3 Marks·Write the answer
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:
Q45Short answer3 Marks·Write the answer
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 20 · asked 2 times · Number systems & binary arithmetic

Compute A - B in 8-bit 2's complement

Q46NAT3 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:
Q47NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Official Key

Master Answer Key & Explanations

Official answer keys from IIT Madras BS past papers. Click any question to review.

Reveal Key

Q14

Q21

Q31

Q43

Q52

Q62

Q72

Q82

Q92

Q101001

Q110

Q120

Q135

Q145

Q15B

Q16B

Q17A

Q18A

Q19A

Q20B

Q21A

Q22A

Q23A

Q24B

Q25A

Q26E

Q27E

Q284

Q295

Q306

Q316

Q323

Q333

Q341000

Q35100

Q3620

Q3718

Q380x09

Q390x06

Q4018

Q4124

Q428

Q434

Q440x2D4D

Q450x2D4D

Q4611101100

Q4711101010

Questions and answer keys are reproduced from the official IIT Madras BS papers. Topics and repeated question types are BTechi’s own grouping. BTechi is not affiliated with IIT Madras.