Question

What is the largest n for which one can solve within one second a problem using an algorithm that requires fin) bit operations, where each bit operation is carried out in 10-9 seconds, with the given functions fin). log n, where the base of the logarithm is 2 Multiple Choice a) 2^10 b) 10^9 c) 2^9 d) 2^10^9

Answer 1

n=210^9.

Step-by-step explanation:

The question is asking for the largest 'n' for which one can solve a problem in one second using an algorithm that requires f(n) bit operations, where each bit operation is carried out in 10-9 seconds, given that f(n)=log n (base 2).

Given that each operation requires 10-9 seconds, we can solve 109 operations in one second. Therefore, we need to solve for n in the equation f(n)=109, which is log2n=109. The solution to this is n=210^9. Hence, the largest 'n' for which one can solve the problem in one second using the given algorithm is 210^9 (option d).