Stage 3 | HeadsTails.java (Game: nine heads and tails) Nine coins are placed in a 3-by-3 matrix with some

face up and some face down. You can represent the state of the coins using a 3-by-3 matrix with values 0 (heads) and 1 (tails). Here are some examples:

0 0 0 1 0 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 1 1

0 0 0 1 0 0 0 0 1 1 0 0 1 1 0

Each state can also be represented using a binary number. For example, the preceding

matrices correspond to the numbers

000010000 101001100 110100001 101110100 100111110

There are a total of 512 possibilities, so you can use decimal numbers 0, 1, 2, 3, . . . , and 511 to represent all states of the matrix. Write a program that prompts the user to enter a number between 0 and 511 and displays the corresponding matrix with the characters H and T. Here is a sample run:

Enter a number between 0 and 511: 7

H H H

H H H

T T T

The user entered 7, which corresponds to 000000111. Since 0 stands for H and

1 for T, the output is correct.

General Algorithm:

Input num

Convert decimal value num to binary in form of 9 bits (make it a method)

Create the 3 X 3 array

Assign H or T based on the binary representation. (make it a method)

Print the matrix

STAGE 4 | Testing

Compile HeadsTails.java and fix syntax errors.

Run the program and Fix runtime and logical errors.