Questions$/$Problems

Computer A can execute a set of instructions in $0\mathrm{.}001$ milliseconds. If the same set of instructions runs on computer B$,$ it will take $0\mathrm{.}03$ microseconds. By what order of magnitude is computer B faster than computer A$?$ Show your solution $(10$ pts$).$

Assuming we define Moore$$s Law as the doubling of microprocessor power every $18$ months, answer the following a$)$ After successfully completing your computer organization and architecture class, you have a brilliant idea for a new chip design that would make a processor six times faster than the fastest ones on the market today. Unfortunately, it will take you four and a half years to save the money, create the prototype, and build a finished product. If Moore$$s Law holds, should you spend your money developing and producing your chip or invest in some other venture?

$2.$ b$)$ Suppose we have a problem that currently takes $100,000$ hours of computer time using current technology to solve. Which of the following would give us the solution first: $(1)$ Replace the algorithm used in the current solution with one that runs twice as fast and run it on the current technology, or $(2)$ Wait three years, assuming Moore$$s Law doubles the performance of a computer every $18$ months, and find the solution using the current algorithm with the new technology?

If a computer has a computational power of $10$ million instructions per second, how long will it take this computer to complete a task that contains $100,000$ instructions? Show your work $(10$ pts$).$

Supposing the doubling of microprocessors' power every $18$ months $($Moor$\text{'}$s Law$)$ holds to date, and the processing power of computers was only $100$ instructions per second when the law was coined $(1965),$ what would be the processing power of the current computers $(2024)?$ Show your solutions $(10$ pts$).$