The U.S. Postal Service printed a bar code on every envelope that represented a five- (or...

The U.S. Postal Service printed a bar code on every envelope that represented a five- (or more) digit zip code using a format called POSTNET (this format was deprecated in favor of a new system, OneCode, in 2009). The bar code consists of long and short bars as shown:

For this program, we will represent the bar code as a string of digits. The digit 1 represents a long bar, and the digit 0 represents a short bar. Therefore, the bar code would be represented in our program as

110100101000101011000010011

The first and last digits of the bar code are always 1. Removing these leaves 25 digits. If these 25 digits are split into groups of 5 digits each, we have

10100  10100 01010  11000  01001

Next, consider each group of 5 digits. There will always be exactly two Is in each group of digits. Each digit stands for a number. From left to right, die digits encode the values 7, 4, 2, 1, and 0. Multiply the corresponding value with the digit and compute the sum to get the final encoded digit for the zip code. The table below shows the encoding for 10100.

Zip Code Digit = 7 + 0 + 2 + 0 + 0 = 9

Repeat this for each group of 5 digits and concatenate to get die complete zip code. There is one special value. If the sum of a group of 5 digits is 11, then this represents the digit 0 (this is necessary because with two digits per group it is not possible to represent zero). The zip code for the sample bar code decodes to 99504. Although die POSTNET scheme may seem unnecessarily complex, its design allows machines to detect if errors have been made in scanning the zip code.

Write a zip code class that encodes and decodes 5-digit bar codes used by the U.S. Postal Service on envelopes. The class should have two constructors. The first constructor should input the zip code as an integer, and the second constructor should input the zip code as a bar code string consisting of 0 s and Is, as described above. Although you have two ways to input the zip code, internally, the class should store the zip code using only one format (you may choose to store it as a bar code string or as a zip code number). The class should also have at least two public member functions, one to return the zip code as an integer, and the other to return the zip code in bar code format as a string. All helper functions should be declared private. Embed your class definition in a suitable test program. Your program should print an error message if an invalid bar code is passed to the constructor.