NPTEL Digital System Design Week 1 Assignment Answers 2025

NPTEL Digital System Design Week 1 Assignment Answers 2025

1. Which of the following best describes “Digital”?

• Continuous and smooth in values and time
• Discrete and discontinuous in nature
• A combination of continuous values forming numbers
• Analog representation of digits

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2. What are the two key steps involved in converting an analog signal into a digital signal?

• Sampling and modulation
• Quantization and filtering
• Discretization in time (sampling) and discretization of values (quantization)
• Amplification and discretization

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3. What is the primary difference between positional and non-positional number systems?

• Positional systems use a fixed set of symbols, while non-positional systems use a variable set.
• Positional systems assign values to symbols based on their position, while non-positional systems assign fixed values to symbols.
• Positional systems are more efficient for complex calculations, while non-positional systems are better for simple arithmetic.
• Positional systems are based on a specific base (like 10), while non-positional systems do not have a fixed base.

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4. What is the decimal equivalent of the binary number (110.011)₂?

• 6.5
• 6.375
• 5.25
• 7.125

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5. What is the binary equivalent of the decimal number 45?

• (101101)₂
• (110101)₂
• (101011)₂
• (11101)₂

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6. What is the hexadecimal equivalent of the binary number 1001 1110?

• 0x9E
• 0xE9
• 0x1E9
• 0x9E1

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7. Perform the binary subtraction 1101₂−100₂. What is the result?

• 1011₂
• 1001₂
• 10011₂
• 100₂

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8. When does overflow occur in addition?

• When the signs of both operands are the same, and the result has the opposite sign.
• When the signs of both operands are different.
• When the result is always positive.
• Overflow can never occur during addition

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9. What happens when converting a 4-bit number to an 8-bit number using sign extension?

• The least significant bit is repeated.
• The most significant bit is extended to fill the extra bits.
• All extra bits are filled with zeros.
• The number remains unchanged.

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10. Assume an 8-bit number and an offset of 127. Represent the value (−45)₁₀
in Sign Magnitude, 1’s Complement, 2’s Complement, and Offset Notation in the same order.

• 10101101, 11010010, 11010011, 01010010
• 10101101, 10101010, 10101011, 01001010
• 10101101, 11010010, 11010011, 01001010
• 10101101, 10101010, 10101100, 01010010

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11. Find the minimum number of bits required to represent the decimal -352 in 2’s complement.

• 8
• 9
• 10
• 7

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12. What is the hexadecimal representation of the sum of (3F2)₁₆+(11010110111010110101)₂?

• 0xD774F
• 0xD7750
• 0xD72A7
• 0xD8747

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13. What is the decimal number represented by the BCD code: 0110010010010101.1001?

• 6549.9
• 6594.9
• 6459.9
• 6495.9

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14. Perform the following operations:

1. Convert 3A7₁₆ to binary.
2. Subtract 1101100111(binary) from the binary equivalent of 3A7₁₆

.3. Convert the resulting binary number back to hexadecimal.

What is the final hexadecimal result?

• 30₁₆
• 40₁₆
• 50₁₆
• 20₁₆

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15. What is the 2’s complement representation of the decimal number −29 in an 8-bit ?

• 11100110₂
• 11100101₂
• 11100011₂
• 11011101₂

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