On What Base Do You Stand?

Introduction

There are times you have to work with some numbers not from the usual bases (like base10, base2, base16). The easiest way to handle them is to convert to base10, but .NET has no built in solution for that...

I will provide one...

Background

The trigger for this small tip was a QA question, that was solved by different poeple in different ways - none of them statisfied me :-)...

Using the Code

static decimal ToBase10(string Value, string BaseChars)
{
  int nBase = BaseChars.Length;
  decimal nResult = 0;
  int nPos = Value.Length - 1;

  foreach (char chDigit in Value.ToUpper().ToArray())
  {
    nResult += (decimal)Math.Pow(nBase, nPos) * BaseChars.ToUpper().IndexOf(chDigit);

    nPos--;
  }

  return (nResult);
}

This code can be used anywhere in your code, in the most simplest way - call it...

decimal base10 = ToBase10("YYY", "XYZ"); // the result is 13, and I will explain it promptly...

Samples and Explanation

Let's start with the parameters of the method...

• Value - it is the basen value to be converted to base10
• BaseChars - a string containing the 'digits' - in order - used in the specific base

Note: For a single digit you can use only a single sign, but any sign!

Now let's see some samples...

Base3 in Different Way...

ToBase10("YYY", "XYZ");

This is a base3 number where the 'digits' to use are X, Y, Z (instead of 0, 1, 2 as we would do normally)... So, following the rules of math, the value of this number is:

$3^{0} * Y + 3^{1} * Y + 3^{2} * Y = Y + 3 * Y + 9 * Y = 13 * Y$

Y is the second 'digit' in this sample, so it's true value is 1... So the final resutl is 13!

Base36 - English numerics...

ToBase10("ENGLISH", "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ");

The base is now 36 (26 letters and 10 digits), so the computation goes like this:

$36^{0} * H + 36^{1} * S + 36^{2} * I + 36^{3} * L + 36^{4} * G + 36^{5} * N + 36^{6} * E = $

$1 * H + 36 * S + 1296 * I + 46656 * L + 1679616 * G + 60466176 * N + 2176782336 * E$

The values of the 'digits' according their position are:

$E = 14, N = 23, G = 16, L = 21, I = 18, S = 28, H = 17$

Inserting these into the equation, you will have 31,893,552,737 as result - a nice number...

Base10 - Can You Recognize?

ToBase10("(!", "!@#$%^&*()");

It is 80, but I will not explain why...that's for you...