NPTEL Computer Architecture Week 8 Assignment Answers 2024

NPTEL Computer Architecture Week 8 Assignment Answers 2024

1. In the equation N=DQ+R, which represents the division of N by D with quotient Q and remainder R, which of the following statements is incorrect? All the numbers (N, D, Q, R) are positive.

• R < D
• R >= 0
• Q is the largest positive integer that satisfies the given equation
• R > D

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2. The time complexity of the Restoring algorithm to divide two n-bit numbers is ____________.

• O(n log(n))
• O(n)
• O(n²)
• O(log(n))

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3. What is the result of 0111 ÷ 0011 using non-restoring division?

• Q = 0010 and R = 0001
• Q = 0011 and R = 0010
• Q = 0100 and R = 0001
• None of the options

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4. What is the result of 1.01 x 2³ + 1.11 x 2²? Assume that the bias is 0 in the normalized-form representation of a floating-point number.

• 1.0001 x 2⁴
• 1.0001 x 2⁵
• 1.0011 x 2⁴
• 1.0111 x 2⁴

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5. What is the correct representation of the normalized form of a 32-bit (denormal) floating-point number in the IEEE 754 format?

• (−1)^S × P × 2⁻¹²⁶ where (0 ≤ P < 1)
• (−1)^S × P × 2⁻¹²⁶ where (1 ≤ P < 2)
• (−1)^S × P × 2⁻¹²⁷ where (0 ≤ P < 1)
• None of the options

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6. What role does the derivative f′(x) play in the Newton-Raphson method?

• It determines the next guess based on the function’s slope to find the root of f(x).
• It determines the distance from the initial guess to the root.
• It is only used when the function is quadratic.
• None of the options.

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7. The time complexity of division using the Newton-Raphson method is __.

• O((n log(n))²)
• O(n log(n))
• O((log(n))²)
• None of the options

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8. Which of the following statements is correct for Goldschmidt division and Newton-Raphson division?

• Goldschmidt division relies on reciprocal approximation, while Newton-Raphson relies on tangent lines.
• The worst-case time complexity of Goldschmidt division is higher than that of the Newton-Raphson method.
• Goldschmidt division uses only subtraction, while Newton-Raphson uses only multiplication.
• None of the options.

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9. The IEEE 754 format supports ___________ rounding modes.

• Four
• Three
• One
• None of the options.

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10. In the truncation rounding mode in IEEE 754, what is the result of truncating -1.5?

• -2
• -1
• -1.5
• None of the options

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