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public class NumeralSystem
{
    public NumeralSystem(string literalString, bool caseSensitive)
    	: this(literalString.ToCharArray(), caseSensitive)
    {
    }

public NumeralSystem(char[] literals, bool caseSensitive)
{
	this.IsCaseSensitive = caseSensitive;
	if (literals.Length == 0)
		throw new ArgumentException("A numeral system must contain some literals.", "literalString");
	HashSet<string> set = new HashSet<string>(new string(literals).Select(c => c.ToString()));
	if (set.Count != literals.Length)
		throw new ArgumentException("Duplicate literals not allowed.", "literalString");
	this.literals = literals;
	if (!this.IsCaseSensitive)
	{
		this.literalsIgnoreCase = literals.Select(c => char.ToLower(c)).ToArray();
	}
}

private char[] literals = new char[0];
private char[] literalsIgnoreCase = new char[0];


public bool IsCaseSensitive { get; private set; }


public string Encode(Int64 value)
{
	if (value < 0)
		throw new ArgumentException("Negative numbers not supported.", "value");
	return this.Encode((UInt64)value);
}

public string Encode(UInt64 value)
{
	string s = string.Empty;
	while (value >= (UInt64)this.literals.Length)
	{
		UInt64 m = value % (UInt64)this.literals.LongLength;
		s = this.literals[m] + s;
		value = value / (UInt64)this.literals.Length;
	}
	s = this.literals[value] + s;
	return s;
}

public string Encode(Int32 value)
{
	if (value < 0)
		throw new ArgumentException("Negative numbers not supported.", "value");
	return this.Encode((UInt32)value);
}

public string Encode(UInt32 value)
{
	string s = string.Empty;
	while (value >= this.literals.Length)
	{
		var m = value % this.literals.Length;
		s = this.literals[m] + s;
		value = value / (UInt32)this.literals.Length;
	}
	s = this.literals[value] + s;
	return s;
}

public string Encode(NumeralSystem fromSystem, string value)
{
	return this.Encode(fromSystem.DecodeToUInt32(value));
}



public Int64 DecodeToUInt64(string value)
{
	if (value == null)
		throw new ArgumentNullException("value");
	Int64 result = 0;
	int i = 0;
	foreach (char ch in value.Reverse())
	{
		int index;
		if (this.IsCaseSensitive)
			index = Array.IndexOf<char>(this.literals, ch);
		else
			index = Array.IndexOf<char>(this.literalsIgnoreCase, char.ToLowerInvariant(ch));
		if (index == -1)
			throw new ApplicationException(string.Format("Invalid character {0}. Valid characters are: {1}.", ch, new String(this.literals)));
		result += index * (int)Math.Pow(this.literals.Length, i);
		i++;
	}
	return result;
}


public UInt32 DecodeToUInt32(string value)
{
	if (value == null)
		throw new ArgumentNullException("value");
	UInt32 result = 0;
	int i = 0;
	foreach (char ch in value.Reverse())
	{
		int index;
		if (this.IsCaseSensitive)
			index = Array.IndexOf<char>(this.literals, ch);
		else
			index = Array.IndexOf<char>(this.literalsIgnoreCase, char.ToLowerInvariant(ch));
		if (index == -1)
			throw new ApplicationException(string.Format("Invalid character {0}. Valid characters are: {1}.", ch, new String(this.literals)));
		result += (uint)index * Convert.ToUInt32(Math.Pow(this.literals.Length, i));
		i++;
	}
	return result;
}


public static NumeralSystem Hexadecimal
{
	get
	{
		return new NumeralSystem("0123456789ABCDEF", false);
	}
}

public static NumeralSystem Octal
{
	get
	{
		return new NumeralSystem("01234567", false);
	}
}

public static NumeralSystem Binary
{
	get
	{
		return new NumeralSystem("01", false);
	}
}

public static NumeralSystem Base36
{
	get
	{
		return new NumeralSystem("0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ", false);
	}
}



public static NumeralSystem Base62
{
	get
	{
		return new NumeralSystem("0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz", true);
	}
}

Example:

string myBase36String = NumeralSystem.Base36.Encode(81271);
// myBase36String will now contain: '1QPJ'
uint i = NumeralSystem.Base36.DecodeToUInt32(myBase36String);

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