discrete math ### Bit Operation Problem Analysis#### 16. Determining the Largest `n` for Daily Computation**Context:** Given an algorithm that requires `f(n)` bit operations, each taking $10^{-11}$ seconds, determine the largest `n` that can be solved within a day for the following functions:- **a)** $\log n$- **b)** $1000n$- **c)** $n^2$- **d)** $1000n^2$- **e)** $n^3$- **f)** $2^n$- **g)** $2^2n$- **h)** $2^{2^n}$#### 17. Determining the Largest `n` for Minute Computation**Context:** Given an algorithm that requires `f(n)` bit operations, each taking $10^{-12}$ seconds, determine the largest `n` that can be solved within a minute for the following functions:- **a)** $\log \log n$- **b)** $\log n$- **c)** $(\log n)^2$**Note:** These problems involve understanding computational limits and the complexity of algorithms given constraints on time and computational resources.

Consider the provided question, Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you that means 16. (a), (b), (c). If you want remaining sub-parts to be solved, then please resubmit the whole question and specify those sub-parts you want us to solve. (16) (a) Each bit operation is carried out in 10-11seconds. T=10-11 seconds. The algorithm can take at most 1 day which contains 24×60×60=86400 seconds, while there are tT=8640010-11=8.64×1015 possible bit operation in 86400 seconds.Algorithm requires f(n)=logn bit operations: logn=8.64×1015 Since, the algorithm has base 2, because bits only have 2 possible values. log2n=8.64×1015 Now, use the property logax=b⇒x=ab So, n=28.64×1015Thus, n=28.64×1015 (b) Each bit operation is carried out in 10-11seconds. T=10-11 seconds. The algorithm can take at most 1 day which contains 24×60×60=86400 seconds, while there are tT=8640010-11=8.64×1015 possible bit operation in 86400 seconds. Algorithm requires f(n)=1000n bit operations: 1000n=8.64×1015⇒n=8.64×10151000⇒n=8.64×1012Thus, n=8.64×1012 (c) Each bit operation is carried out in 10-11seconds. T=10-11 seconds. The algorithm can take at most 1 day which contains 24×60×60=86400 seconds, while there are tT=8640010-11=8.64×1015 possible bit operation in 86400 seconds. Algorithm requires f(n)=n2 bit operations: n2=8.64×1015⇒n=8.64×1015⇒n≈9.295×107Thus, n≈9.295×107

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What is the largest n for which one can solve within a day using an algorithm that requires f (n) bit operations, where each bit operation is carried out in 10" seconds, with these functions f (n)? a) log n b) 1000n c) n²

What is the largest n for which one can solve within a day using an algorithm that requires f (n) bit operations, where each bit operation is carried out in 10" seconds, with these functions f (n)? a) log n b) 1000n c) n²

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

discrete math

### Bit Operation Problem Analysis

#### 16. Determining the Largest `n` for Daily Computation

**Context:**
Given an algorithm that requires `f(n)` bit operations, each taking $10^{-11}$ seconds, determine the largest `n` that can be solved within a day for the following functions:

- **a)** $\log n$
- **b)** $1000n$
- **c)** $n^2$
- **d)** $1000n^2$
- **e)** $n^3$
- **f)** $2^n$
- **g)** $2^2n$
- **h)** $2^{2^n}$

#### 17. Determining the Largest `n` for Minute Computation

**Context:**
Given an algorithm that requires `f(n)` bit operations, each taking $10^{-12}$ seconds, determine the largest `n` that can be solved within a minute for the following functions:

- **a)** $\log \log n$
- **b)** $\log n$
- **c)** $(\log n)^2$

**Note:** These problems involve understanding computational limits and the complexity of algorithms given constraints on time and computational resources.

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