Nine coins are placed in a 3-by-3 matrix with some face up and some face down. You can rep...

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:

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

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:

The user entered 7, which corresponds to 000000111. Since 0 stands for H and 1 for T, the output is correct.