Introduction to Algorithms
Week 1: Exercises

These are optional exercises for practicing the concepts we learned this week.

1. Powers of Two

What is the approximate value of

a) 2¹⁴

b) 2³²

c) 8⁸

2. Logarithms

What is the approximate value of

a) log₂(8,000,000,000)

b) log₁₆(16,000,000)

3. A Slow Connection

A notebook computer's disk holds 500 Gb of data. We would like to send the data across an extremely slow network that transfers only 1 byte/second. Approximately how long will the transfer take?

4. Squares Mod 4

Is this statement true or false?

For all n ∈ ℤ, n² mod 4 < 2.

Prove your answer.