Solution

The correct answer is 1.5 hour

Key PointsTo determine how much time an algorithm using 2⁵⁰ bit operations needs if each bit operation takes 2^-38 seconds, we can follow these steps:

Calculate the total time: \(\text{Total time} = (\text{number of bit operations}) \times (\text{time per bit operation})\)

Substitute the given values: \(\text{Total time} = 2^{50} \times 2^{-38}\)

Simplify the expression: \(2^{50} \times 2^{-38} = 2^{(50-38)} = 2^{12}\)

Compute \(2^{12}\): \(2^{12} = 4096 \text{ seconds}\)

Convert 4096 seconds to minutes and hours: \(4096 \text{ seconds} \div 60 \approx 68.27 \text{ minutes}\)  \(68.27 \text{ minutes} \div 60 \approx 1.1378 \text{ hours}\)

This is slightly more than 1 hour but less than 1.5 hours.
The closest and most appropriate choice is: 4) 1.5 hour