## 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(n
^{2}) - 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 2^{3} + 1.11 x 2^{2}? Assume that the bias is 0 in the normalized-form representation of a floating-point number.

- 1.0001 x 2
^{4} - 1.0001 x 2
^{5} - 1.0011 x 2
^{4} - 1.0111 x 2
^{4}

Answer :-

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

Answer :-

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.

Answer :-

9. The IEEE 754 format supports ___________ rounding modes.

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

Answer :-

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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