CS401 Lab 2

CS401 Lab 2: Expressions And Control Structures

Introduction

This lab will give you practice using the expressions and control structures that we discussed in lecture. Recall that expressions are parts of statements that instruct the computer to perform some computation. We also starting looking at if and switch control structures along with while, do, and for looping structures. Furthermore, we also discussed the Scanner class for obtaining input from the user.

Idea

A Logarithm is a very useful mathematical function. Using a given base, b, we define Y = log_b X to be the exponent such that b^Y = X. For example, with b = 10:

log₁₀ 123456 = 5.091512206277716810 meaning 10^{5.091512206277716810} = 123456

If we're dealing strictly with integer values, then we obviously need to round this value using a floor or ceiling function. For the purposes of this lab, consider the floor function such that:

floor(log₁₀ 123456) = 5 floor(log₂ 128) = 7

One way of calculating floor(log_b X) is by repeated integer division. Continually divide by b until the quotient is less than the base. The number of divisions performed is equal to the result of the floor of the log. For example:

123456 / 10 = 12345 / 10 = 1234 / 10 = 123 / 10 = 12 / 10 = 1 => 5 divisions 128 / 2 = 64 / 2 = 32 / 2 = 16 / 2 = 8 / 2 = 4 / 2 = 2 / 2 = 1 => 7 divisions

Program Details

Write a Java program that computes the floor of the log as described above. Your program should do the following:

Ask the user to enter an integer base, b > 1
Ask the user to enter a positive integer X. If the user enters a number less than zero, it should be rejected, the user should be prompted to reenter the number
Calculates the floor of log_b X by repeated division
Prints the result
Repeats the above steps until the user enters a number less than 1 for the base, b

Test your program with different inputs to be sure it all works correctly. When done, submit it to the lab2 subdirectory of the course submissions site.

Hints

You'll need to use nested loops for this problem. However, the exact combination of loops can very from solution to solution. Spend some time planning how you're program is going to work. Look at the class examples posted on the course website for help.