Project 3 Stacks Solution

Purpose
The purpose of this assignment is to gain experience with the Stack<T> class in converting non-negative decimal integers into a different base between 2 and 16.  
The Problem
Decimal to a New Base (2 …16)
One way to convert a non-negative decimal (base 10) integer to a new base (2 - 16) is described here.  
If Base is the new base and N is the number to be converted, then 
    • (integer) divide N by Base to get both an integer quotient and an integer remainder.  
    • Place the remainder in a Stack, and repeat the process on the quotient until quotient == zero.  
    • Add (push) 0’s to the Stack if necessary to get the desired number of “digits” in the result.  
    • Then retrieve and output the values on the Stack until it is empty, using the letters A, B, C, D, E, and F for remainders of more than one digit (i.e., 10, 11, 12, 13, 14, and 15, respectively).  Use an array to make matching the remainder with its proper representation easy.
Example 1 – Decimal to Binary (Base 2)
For example, the decimal number 123 can be converted to binary (base 2) as follows:
123 / 2     = 61 with a remainder of 1; push 1 onto the Stack
61 / 2         = 30 with a remainder of 1; push 1 onto the Stack
30 / 2         = 15 with a remainder of 0; push 0 onto the Stack
15 / 2         = 7 with a remainder of 1; push 1 onto the Stack
7 / 2         = 3 with a remainder of 1; push 1 onto the Stack
3 / 2         = 1 with a remainder of 1; push 1 onto the Stack
1 / 2         = 0 with a remainder of 1; push 1 onto the Stack
The quotient is now 0 so we can quit.  
The Stack contains the remainders 1, 1, 1, 1, 0, 1, 1 in that order.  If our goal is an 8-bit result, we push one more 0 onto the Stack to get 8 bits, resulting in 0, 1, 1, 1, 1, 0, 1, 1 being the values on the Stack in that order.  Popping the Stack and outputting the result until the Stack is empty yields a binary value of
01111011
Example 2 – Decimal to Hexadecimal (Base 16) 
To convert the same number (decimal 123) to hexadecimal (base 16), we do the following:
        123 / 16    = 7 with a remainder of 11; push B onto the Stack
        7 / 16        = 0 with a remainder of 7; push 7 onto the Stack
Now, if we want to have a 16-bit (2-byte) result, we have to add 2 leading 0’s by pushing them into the Stack, with a result of the Stack containing 0, 0, 7, B in that order.  The answer is thus: 007B.
Use .NET’s Stack<T> class to implement the stack described here.

From another base (2 … 16) to decimal
To convert an unsigned integer number in the opposite direction (i.e., to convert a number in base Base back to decimal (base 10) form), process the number one digit at a time, left to right.  
    • Start by setting the result to 0.  
    • For each digit from left to right, 
        ◦ multiply result by Base
        ◦ add the next digit (adding 10 for A, 11 for B, and so forth – using the array lookup method described above) to result  
For example, the octal number (base 8) 123 converts to the decimal number 83 as follows
((1 x 8) + 2) x 8) + 3 = 83
In this example, the octal number 123 represents 
(1 x 82) + (2 x 81) + (3 x 80) = 64 + 16 + 3 = 83
Specifications
Write a C# program that will allow you to convert any non-negative base 10 integer (within the range supported by the 32-bit architecture of a machine) to a specified base between 2 and 16 and to convert any non-negative number in a base between 2 and 16 back into a decimal number (i.e., base 10).  Allow the user to specify the number to be converted, the base to use, and the number of places (“digits”) desired in the output.
Your solution must be a Windows Forms application with its own icon and appropriate controls as illustrated below.  The title in the caption bar should be obtained from your AssemblyInfo.cs file.
  

The solution should include a BaseConverter class with static methods named ToDecimal and FromDecimal.  Use these methods in your main program to do the required conversions.  ToDecimal should return an integer whereas FromDecimal should return a string.  Both returned values should contain the proper representations of the numbers in question.  The parameters for both are the numbers to be converted in either integer or string format as appropriate to its type.
Use appropriate KeyPress event handlers to prevent invalid input.
When testing this program, be sure to verify that when you convert a decimal number to some other base, then take the answer and convert it back, the result is your original number.  A program with this characteristic may still be incorrect, but it cannot be correct without having this characteristic.
You may add other bells and whistles such as an About box, splash screen, and so forth if you wish as long as you have at least what is specified and as long as the result is user-friendly.
Deliverables
Submit this project as specified in the Course Facts document.  Be sure to send it both to your instructor AND to the course TA.