Question

Write a code segment that creates parallel arrays containing the first 10 nonnegative powers of \(2 .\) One array should contain the exponent and the other array should contain 2 raised to that power.

Short answer

Create two arrays of size 10 and fill them using a loop: one with exponents from 0 to 9, and the other with 2 raised to each exponent.

Step-by-step solution

Initialize the Arrays

Create two arrays, one for storing the exponents and another for storing the powers of 2. Ensure the arrays have a size of 10.

Populate the Exponent Array

Use a loop to fill the exponent array with values from 0 to 9.

Populate the Power of 2 Array

Within the same loop, calculate the power of 2 for each exponent and store the result in the power of 2 array.

Implement the Code

Write the complete code segment to achieve the above steps. The code should correctly create and populate both arrays.

Key concepts

array initialization in Java

Arrays are an essential part of Java programming. They allow you to group multiple values under a single variable name. To initialize an array in Java, you first declare the array and then allocate memory for it. For this exercise, we create two arrays: one for the exponents and another for the powers of 2. We can initialize these arrays as follows:

int[] exponents = new int[10];
int[] powersOf2 = new int[10];

Here, we declare two integer arrays, each with a size of 10. This means both arrays can store 10 integer values. Once the arrays are initialized, they are ready to be populated with data.

for loop in Java

For loops are incredibly useful when you need to perform repetitive actions. In this exercise, we use a for loop to populate both arrays. A typical for loop in Java looks like this:

for (int i = 0; i < 10; i++) {
    // Code to execute
}

This loop starts with i equal to 0 and increments i by 1 each iteration until i reaches 10. Inside the loop, we can populate the arrays as follows:

for (int i = 0; i < 10; i++) {
    exponents[i] = i;
    powersOf2[i] = (int) Math.pow(2, i);
}

In this code snippet, the loop populates each index of the exponent array with the corresponding value of i and uses the Math.pow method to calculate powers of 2.

power calculation in Java

Calculating powers of numbers is a common task in programming. In Java, you can use the Math.pow method to do this. The syntax is Math.pow(base, exponent).

In this exercise, we need to calculate 2 raised to the power of a given exponent. Here is how you do it:

int result = (int) Math.pow(2, exponent);

The Math.pow method returns a double value, so we cast it to an integer using (int). This ensures the result fits into our arrays of type int. In our for loop, this is executed like so:

powersOf2[i] = (int) Math.pow(2, i);

This line calculates 2 raised to the power of i and stores it in the powersOf2 array.

exponentiation

Exponentiation is the process of raising a base to a given power. In mathematics, it is represented as baseexponent. For example, 2 raised to the power of 3 is written as 23 and equals 8.

In the context of our Java program, we are calculating the first 10 nonnegative powers of 2. This means we want the values of 20, 21, ... , 29. By using the Math.pow(2, exponent) method inside a for loop, we can efficiently compute and store these values in an array.

Here is how the complete code looks after combining all the concepts:

int[] exponents = new int[10];
int[] powersOf2 = new int[10];

for (int i = 0; i < 10; i++) {
    exponents[i] = i;
    powersOf2[i] = (int) Math.pow(2, i);
}

This code correctly initializes the arrays, uses a for loop to populate them, calculates powers of 2, and illustrates the concept of exponentiation in programming.