# Computer Architecture Nptel Week 8 Assignment Answers 2024

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## Table of Contents

**Computer Architecture Nptel Week 8 Assignment Answers (July-Dec 2024)**

**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:**

A) R < D B) R >= 0

C) Q is the largest positive integer that satisfies the given equation

D) R > D

**Answer:** D) R > D

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

A) O(n log(n))

B) O(n)

C) O(n²)

D) O(log(n))

**Answer:** A) O(n log(n))

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

A) Q = 0010 and R = 0001

B) Q = 0011 and R = 0010

C) Q = 0100 and R = 0001

D) None of the options

**Answer:** A) Q = 0010 and R = 0001

**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.**

A) 1.0001 x 2⁴

B) 1.0001 x 2⁵

C) 1.0011 x 2⁴

D) 1.0111 x 2⁴

**Answer:** A) 1.0001 x 2⁴

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

A) (−1)ˢ × P × 2⁻¹²⁶ where (0 ≤ P < 1)

B) (−1)ˢ × P × 2⁻¹²⁶ where (1 ≤ P < 2)

C) (−1)ˢ × P × 2⁻¹²⁷ where (0 ≤ P < 1)

D) None of the options

**Answer:** A) (−1)ˢ × P × 2⁻¹²⁶ where (0 ≤ P < 1)

These are Computer Architecture Nptel Week 8 Assignment Answers

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

A) It determines the next guess based on the function’s slope to find the root of f(x).

B) It determines the distance from the initial guess to the root.

C) It is only used when the function is quadratic.

D) None of the options.

**Answer:** A) It determines the next guess based on the function’s slope to find the root of f(x).

**The time complexity of division using the Newton-Raphson method is _.**

A) O((n log(n))²)

B) O(n log(n))

C) O((log(n))²)

D) None of the options

**Answer:** C) O((log(n))²)

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

A) Goldschmidt division relies on reciprocal approximation, while Newton-Raphson relies on tangent lines.

B) The worst-case time complexity of Goldschmidt division is higher than that of the Newton-Raphson method.

C) Goldschmidt division uses only subtraction, while Newton-Raphson uses only multiplication.

D) None of the options.

**Answer:** A) Goldschmidt division relies on reciprocal approximation, while Newton-Raphson relies on tangent lines.

**The IEEE 754 format supports _ rounding modes.**

A) Four

B) Three

C) One

D) None of the options.

**Answer:** A) Four

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

A) -2

B) -1

C) -1.5

D) None of the options

**Answer:** B) -1

These are Computer Architecture Nptel Week 8 Assignment Answers

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