[c#] Quickest way to convert a base 10 number to any base in .NET?

I have and old(ish) C# method I wrote that takes a number and converts it to any base:

string ConvertToBase(int number, char[] baseChars);

It's not all that super speedy and neat. Is there a good, known way of achieving this in .NET?

I'm looking for something that allows me to use any base with an arbitrary string of characters to use.

This only allows bases 16, 10, 8 and 2:

Convert.ToString(1, x);

I want to use this to achieve a massively high base taking advantage of numbers, all lower case and all upper case letters. Like in this thread, but for C# not JavaScript.

Does anyone know of a good and efficient way of doing this in C#?

This question is related to c# .net int base number-systems

The answer is


Convert.ToString can be used to convert a number to its equivalent string representation in a specified base.

Example:

string binary = Convert.ToString(5, 2); // convert 5 to its binary representation
Console.WriteLine(binary);              // prints 101

However, as pointed out by the comments, Convert.ToString only supports the following limited - but typically sufficient - set of bases: 2, 8, 10, or 16.

Update (to meet the requirement to convert to any base):

I'm not aware of any method in the BCL which is capable to convert numbers to any base so you would have to write your own small utility function. A simple sample would look like that (note that this surely can be made faster by replacing the string concatenation):

class Program
{
    static void Main(string[] args)
    {
        // convert to binary
        string binary = IntToString(42, new char[] { '0', '1' });

        // convert to hexadecimal
        string hex = IntToString(42, 
            new char[] { '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
                         'A', 'B', 'C', 'D', 'E', 'F'});

        // convert to hexavigesimal (base 26, A-Z)
        string hexavigesimal = IntToString(42, 
            Enumerable.Range('A', 26).Select(x => (char)x).ToArray());

        // convert to sexagesimal
        string xx = IntToString(42, 
            new char[] { '0','1','2','3','4','5','6','7','8','9',
            'A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','W','X','Y','Z',
            'a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x'});
    }

    public static string IntToString(int value, char[] baseChars)
    {
        string result = string.Empty;
        int targetBase = baseChars.Length;

        do
        {
            result = baseChars[value % targetBase] + result;
            value = value / targetBase;
        } 
        while (value > 0);

        return result;
    }

    /// <summary>
    /// An optimized method using an array as buffer instead of 
    /// string concatenation. This is faster for return values having 
    /// a length > 1.
    /// </summary>
    public static string IntToStringFast(int value, char[] baseChars)
    {
        // 32 is the worst cast buffer size for base 2 and int.MaxValue
        int i = 32;
        char[] buffer = new char[i];
        int targetBase= baseChars.Length;

        do
        {
            buffer[--i] = baseChars[value % targetBase];
            value = value / targetBase;
        }
        while (value > 0);

        char[] result = new char[32 - i];
        Array.Copy(buffer, i, result, 0, 32 - i);

        return new string(result);
    }
}

Update 2 (Performance Improvement)

Using an array buffer instead of string concatenation to build the result string gives a performance improvement especially on large number (see method IntToStringFast). In the best case (i.e. the longest possible input) this method is roughly three times faster. However, for 1-digit numbers (i.e. 1-digit in the target base), IntToString will be faster.


I recently blogged about this. My implementation does not use any string operations during the calculations, which makes it very fast. Conversion to any numeral system with base from 2 to 36 is supported:

/// <summary>
/// Converts the given decimal number to the numeral system with the
/// specified radix (in the range [2, 36]).
/// </summary>
/// <param name="decimalNumber">The number to convert.</param>
/// <param name="radix">The radix of the destination numeral system (in the range [2, 36]).</param>
/// <returns></returns>
public static string DecimalToArbitrarySystem(long decimalNumber, int radix)
{
    const int BitsInLong = 64;
    const string Digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";

    if (radix < 2 || radix > Digits.Length)
        throw new ArgumentException("The radix must be >= 2 and <= " + Digits.Length.ToString());

    if (decimalNumber == 0)
        return "0";

    int index = BitsInLong - 1;
    long currentNumber = Math.Abs(decimalNumber);
    char[] charArray = new char[BitsInLong];

    while (currentNumber != 0)
    {
        int remainder = (int)(currentNumber % radix);
        charArray[index--] = Digits[remainder];
        currentNumber = currentNumber / radix;
    }

    string result = new String(charArray, index + 1, BitsInLong - index - 1);
    if (decimalNumber < 0)
    {
        result = "-" + result;
    }

    return result;
}

I've also implemented a fast inverse function in case anyone needs it too: Arbitrary to Decimal Numeral System.


Could this class from this forum post help you?

public class BaseConverter { 

public static string ToBase(string number, int start_base, int target_base) { 

  int base10 = this.ToBase10(number, start_base); 
  string rtn = this.FromBase10(base10, target_base); 
  return rtn; 

} 

public static int ToBase10(string number, int start_base) { 

  if (start_base < 2 || start_base > 36) return 0; 
  if (start_base == 10) return Convert.ToInt32(number); 

  char[] chrs = number.ToCharArray(); 
  int m = chrs.Length - 1; 
  int n = start_base; 
  int x; 
  int rtn = 0; 

  foreach(char c in chrs) { 

    if (char.IsNumber(c)) 
      x = int.Parse(c.ToString()); 
    else 
      x = Convert.ToInt32(c) - 55; 

    rtn += x * (Convert.ToInt32(Math.Pow(n, m))); 

    m--; 

  } 

  return rtn; 

} 

public static string FromBase10(int number, int target_base) { 

  if (target_base < 2 || target_base > 36) return ""; 
  if (target_base == 10) return number.ToString(); 

  int n = target_base; 
  int q = number; 
  int r; 
  string rtn = ""; 

  while (q >= n) { 

    r = q % n; 
    q = q / n; 

    if (r < 10) 
      rtn = r.ToString() + rtn; 
    else 
      rtn = Convert.ToChar(r + 55).ToString() + rtn; 

  } 

  if (q < 10) 
    rtn = q.ToString() + rtn; 
  else 
    rtn = Convert.ToChar(q + 55).ToString() + rtn; 

  return rtn; 

} 

}

Totally untested... let me know if it works! (Copy-pasted it in case the forum post goes away or something...)


I too was looking for a fast way to convert decimal number to another base in the range of [2..36] so I developed the following code. Its simple to follow and uses a Stringbuilder object as a proxy for a character buffer that we can index character by character. The code appears to be very fast compared to alternatives and a lot faster than initialising individual characters in a character array.

For your own use you might prefer to: 1/ Return a blank string rather than throw an exception. 2/ remove the radix check to make the method run even faster 3/ Initialise the Stringbuilder object with 32 '0's and remove the the line result.Remove( 0, i );. This will cause the string to be returned with leading zeros and further increase the speed. 4/ Make the Stringbuilder object a static field within the class so no matter how many times the DecimalToBase method is called the Stringbuilder object is only initialised the once. If you do this change 3 above would no longer work.

I hope someone finds this useful :)

AtomicParadox

        static string DecimalToBase(int number, int radix)
    {
        // Check that the radix is between 2 and 36 inclusive
        if ( radix < 2 || radix > 36 )
            throw new ArgumentException("ConvertToBase(int number, int radix) - Radix must be between 2 and 36.");

        // Create a buffer large enough to hold the largest int value represented in binary digits 
        StringBuilder result = new StringBuilder("                                ");  // 32 spaces

        // The base conversion calculates the digits in reverse order so use
        // an index to point to the last unused space in our buffer
        int i = 32; 

        // Convert the number to the new base
        do
        {
            int remainder = number % radix;
            number = number / radix;
            if(remainder <= 9)
                result[--i] = (char)(remainder + '0');  // Converts [0..9] to ASCII ['0'..'9']
            else
                result[--i] = (char)(remainder + '7');  // Converts [10..36] to ASCII ['A'..'Z']
        } while ( number > 0 );

        // Remove the unwanted padding from the front of our buffer and return the result
        // Note i points to the last unused character in our buffer
        result.Remove( 0, i );
        return (result.ToString());
    }

FAST "FROM" AND "TO" METHODS

I am late to the party, but I compounded previous answers and improved over them. I think these two methods are faster than any others posted so far. I was able to convert 1,000,000 numbers from and to base 36 in under 400ms in a single core machine.

Example below is for base 62. Change the BaseChars array to convert from and to any other base.

private static readonly char[] BaseChars = 
         "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz".ToCharArray();
private static readonly Dictionary<char, int> CharValues = BaseChars
           .Select((c,i)=>new {Char=c, Index=i})
           .ToDictionary(c=>c.Char,c=>c.Index);

public static string LongToBase(long value)
{
   long targetBase = BaseChars.Length;
   // Determine exact number of characters to use.
   char[] buffer = new char[Math.Max( 
              (int) Math.Ceiling(Math.Log(value + 1, targetBase)), 1)];

   var i = buffer.Length;
   do
   {
       buffer[--i] = BaseChars[value % targetBase];
       value = value / targetBase;
   }
   while (value > 0);

   return new string(buffer, i, buffer.Length - i);
}

public static long BaseToLong(string number) 
{ 
    char[] chrs = number.ToCharArray(); 
    int m = chrs.Length - 1; 
    int n = BaseChars.Length, x;
    long result = 0; 
    for (int i = 0; i < chrs.Length; i++)
    {
        x = CharValues[ chrs[i] ];
        result += x * (long)Math.Pow(n, m--);
    }
    return result;  
} 

EDIT (2018-07-12)

Fixed to address the corner case found by @AdrianBotor (see comments) converting 46655 to base 36. This is caused by a small floating-point error calculating Math.Log(46656, 36) which is exactly 3, but .NET returns 3 + 4.44e-16, which causes an extra character in the output buffer.


Very late to the party on this one, but I wrote the following helper class recently for a project at work. It was designed to convert short strings into numbers and back again (a simplistic perfect hash function), however it will also perform number conversion between arbitrary bases. The Base10ToString method implementation answers the question that was originally posted.

The shouldSupportRoundTripping flag passed to the class constructor is needed to prevent the loss of leading digits from the number string during conversion to base-10 and back again (crucial, given my requirements!). Most of the time the loss of leading 0s from the number string probably won't be an issue.

Anyway, here's the code:

using System;
using System.Collections.Generic;
using System.Linq;

namespace StackOverflow
{
    /// <summary>
    /// Contains methods used to convert numbers between base-10 and another numbering system.
    /// </summary>
    /// <remarks>
    /// <para>
    /// This conversion class makes use of a set of characters that represent the digits used by the target
    /// numbering system. For example, binary would use the digits 0 and 1, whereas hex would use the digits
    /// 0 through 9 plus A through F. The digits do not have to be numerals.
    /// </para>
    /// <para>
    /// The first digit in the sequence has special significance. If the number passed to the
    /// <see cref="StringToBase10"/> method has leading digits that match the first digit, then those leading
    /// digits will effectively be 'lost' during conversion. Much of the time this won't matter. For example,
    /// "0F" hex will be converted to 15 decimal, but when converted back to hex it will become simply "F",
    /// losing the leading "0". However, if the set of digits was A through Z, and the number "ABC" was
    /// converted to base-10 and back again, then the leading "A" would be lost. The <see cref="System.Boolean"/>
    /// flag passed to the constructor allows 'round-tripping' behaviour to be supported, which will prevent
    /// leading digits from being lost during conversion.
    /// </para>
    /// <para>
    /// Note that numeric overflow is probable when using longer strings and larger digit sets.
    /// </para>
    /// </remarks>
    public class Base10Converter
    {
        const char NullDigit = '\0';

        public Base10Converter(string digits, bool shouldSupportRoundTripping = false)
            : this(digits.ToCharArray(), shouldSupportRoundTripping)
        {
        }

        public Base10Converter(IEnumerable<char> digits, bool shouldSupportRoundTripping = false)
        {
            if (digits == null)
            {
                throw new ArgumentNullException("digits");
            }

            if (digits.Count() == 0)
            {
                throw new ArgumentException(
                    message: "The sequence is empty.",
                    paramName: "digits"
                    );
            }

            if (!digits.Distinct().SequenceEqual(digits))
            {
                throw new ArgumentException(
                    message: "There are duplicate characters in the sequence.",
                    paramName: "digits"
                    );
            }

            if (shouldSupportRoundTripping)
            {
                digits = (new[] { NullDigit }).Concat(digits);
            }

            _digitToIndexMap =
                digits
                .Select((digit, index) => new { digit, index })
                .ToDictionary(keySelector: x => x.digit, elementSelector: x => x.index);

            _radix = _digitToIndexMap.Count;

            _indexToDigitMap =
                _digitToIndexMap
                .ToDictionary(keySelector: x => x.Value, elementSelector: x => x.Key);
        }

        readonly Dictionary<char, int> _digitToIndexMap;
        readonly Dictionary<int, char> _indexToDigitMap;
        readonly int _radix;

        public long StringToBase10(string number)
        {
            Func<char, int, long> selector =
                (c, i) =>
                {
                    int power = number.Length - i - 1;

                    int digitIndex;
                    if (!_digitToIndexMap.TryGetValue(c, out digitIndex))
                    {
                        throw new ArgumentException(
                            message: String.Format("Number contains an invalid digit '{0}' at position {1}.", c, i),
                            paramName: "number"
                            );
                    }

                    return Convert.ToInt64(digitIndex * Math.Pow(_radix, power));
                };

            return number.Select(selector).Sum();
        }

        public string Base10ToString(long number)
        {
            if (number < 0)
            {
                throw new ArgumentOutOfRangeException(
                    message: "Value cannot be negative.",
                    paramName: "number"
                    );
            }

            string text = string.Empty;

            long remainder;
            do
            {
                number = Math.DivRem(number, _radix, out remainder);

                char digit;
                if (!_indexToDigitMap.TryGetValue((int) remainder, out digit) || digit == NullDigit)
                {
                    throw new ArgumentException(
                        message: "Value cannot be converted given the set of digits used by this converter.",
                        paramName: "number"
                        );
                }

                text = digit + text;
            }
            while (number > 0);

            return text;
        }
    }
}

This can also be subclassed to derive custom number converters:

namespace StackOverflow
{
    public sealed class BinaryNumberConverter : Base10Converter
    {
        public BinaryNumberConverter()
            : base(digits: "01", shouldSupportRoundTripping: false)
        {
        }
    }

    public sealed class HexNumberConverter : Base10Converter
    {
        public HexNumberConverter()
            : base(digits: "0123456789ABCDEF", shouldSupportRoundTripping: false)
        {
        }
    }
}

And the code would be used like this:

using System.Diagnostics;

namespace StackOverflow
{
    class Program
    {
        static void Main(string[] args)
        {
            {
                var converter = new Base10Converter(
                    digits: "ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789abcdefghijklmnopqrstuvwxyz",
                    shouldSupportRoundTripping: true
                    );

                long number = converter.StringToBase10("Atoz");
                string text = converter.Base10ToString(number);
                Debug.Assert(text == "Atoz");
            }

            {
                var converter = new HexNumberConverter();

                string text = converter.Base10ToString(255);
                long number = converter.StringToBase10(text);
                Debug.Assert(number == 255);
            }
        }
    }
}

I was using this to store a Guid as a shorter string (but was limited to use 106 characters). If anyone is interested here is my code for decoding the string back to numeric value (in this case I used 2 ulongs for the Guid value, rather than coding an Int128 (since I'm in 3.5 not 4.0). For clarity CODE is a string const with 106 unique chars. ConvertLongsToBytes is pretty unexciting.

private static Guid B106ToGuid(string pStr)
    {
        try
        {
            ulong tMutl = 1, tL1 = 0, tL2 = 0, targetBase = (ulong)CODE.Length;
            for (int i = 0; i < pStr.Length / 2; i++)
            {
                tL1 += (ulong)CODE.IndexOf(pStr[i]) * tMutl;
                tL2 += (ulong)CODE.IndexOf(pStr[pStr.Length / 2 + i]) * tMutl;
                tMutl *= targetBase;
            }
            return new Guid(ConvertLongsToBytes(tL1, tL2));
        }
        catch (Exception ex)
        {
            throw new Exception("B106ToGuid failed to convert string to Guid", ex);
        }
    }

One can also use slightly modified version of the accepted one and adjust base characters string to it's needs:

public static string Int32ToString(int value, int toBase)
{
    string result = string.Empty;
    do
    {
        result = "0123456789ABCDEF"[value % toBase] + result;
        value /= toBase;
    }
    while (value > 0);

    return result;
}

This is a fairly straightforward way to do this, but it may not be the fastest. It is quite powerful because it is composable.

public static IEnumerable<int> ToBase(this int x, int b)
{
    IEnumerable<int> ToBaseReverse()
    {
        if (x == 0)
        {
            yield return 0;
            yield break;
        }
        int z = x;
        while (z > 0)
        {
            yield return z % b;
            z = z / b;
        }
    }

    return ToBaseReverse().Reverse();
}

Combine this with this simple extension method and any getting any base is now possible:

public static string ToBase(this int number, string digits) =>
    String.Concat(number.ToBase(digits.Length).Select(x => digits[x]));

It can be used like this:

var result = 23.ToBase("01");
var result2 = 23.ToBase("012X");

Console.WriteLine(result);
Console.WriteLine(result2);

The output is:

10111
11X

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConvertToAnyBase
{
   class Program
    {
        static void Main(string[] args)
        {
            var baseNumber = int.Parse(Console.ReadLine());
            var number = int.Parse(Console.ReadLine());
            string conversion = "";


            while(number!=0)
            {

                conversion += Convert.ToString(number % baseNumber);
                number = number / baseNumber;
            }
            var conversion2 = conversion.ToArray().Reverse();
            Console.WriteLine(string.Join("", conversion2));


       }
    }
}

If anyone is seeking a VB option, this was based on Pavel's answer:

Public Shared Function ToBase(base10 As Long, Optional baseChars As String = "0123456789ABCDEFGHIJKLMNOPQRTSUVWXYZ") As String

    If baseChars.Length < 2 Then Throw New ArgumentException("baseChars must be at least 2 chars long")

    If base10 = 0 Then Return baseChars(0)

    Dim isNegative = base10 < 0
    Dim radix = baseChars.Length
    Dim index As Integer = 64 'because it's how long a string will be if the basechars are 2 long (binary)
    Dim chars(index) As Char '65 chars, 64 from above plus one for sign if it's negative

    base10 = Math.Abs(base10)


    While base10 > 0
        chars(index) = baseChars(base10 Mod radix)
        base10 \= radix

        index -= 1
    End While

    If isNegative Then
        chars(index) = "-"c
        index -= 1
    End If

    Return New String(chars, index + 1, UBound(chars) - index)

End Function

I had a similar need, except I needed to do math on the "numbers" as well. I took some of the suggestions here and created a class that will do all this fun stuff. It allows for any unicode character to be used to represent a number and it works with decimals too.

This class is pretty easy to use. Just create a number as a type of New BaseNumber, set a few properties, and your off. The routines take care of switching between base 10 and base x automatically and the value you set is preserved in the base you set it in, so no accuracy is lost (until conversion that is, but even then precision loss should be very minimal since this routine uses Double and Long where ever possible).

I can't command on the speed of this routine. It is probably quite slow, so I'm not sure if it will suit the needs of the one who asked the question, but it certain is flexible, so hopefully someone else can use this.

For anyone else that may need this code for calculating the next column in Excel, I will include the looping code I used that leverages this class.

Public Class BaseNumber

    Private _CharacterArray As List(Of Char)

    Private _BaseXNumber As String
    Private _Base10Number As Double?

    Private NumberBaseLow As Integer
    Private NumberBaseHigh As Integer

    Private DecimalSeparator As Char = System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NumberDecimalSeparator
    Private GroupSeparator As Char = System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NumberGroupSeparator

    Public Sub UseCapsLetters()
        'http://unicodelookup.com
        TrySetBaseSet(65, 90)
    End Sub

    Public Function GetCharacterArray() As List(Of Char)
        Return _CharacterArray
    End Function

    Public Sub SetCharacterArray(CharacterArray As String)
        _CharacterArray = New List(Of Char)
        _CharacterArray.AddRange(CharacterArray.ToList)

        TrySetBaseSet(_CharacterArray)
    End Sub

    Public Sub SetCharacterArray(CharacterArray As List(Of Char))
        _CharacterArray = CharacterArray
        TrySetBaseSet(_CharacterArray)
    End Sub

    Public Sub SetNumber(Value As String)
        _BaseXNumber = Value
        _Base10Number = Nothing
    End Sub

    Public Sub SetNumber(Value As Double)
        _Base10Number = Value
        _BaseXNumber = Nothing
    End Sub

    Public Function GetBaseXNumber() As String
        If _BaseXNumber IsNot Nothing Then
            Return _BaseXNumber
        Else
            Return ToBaseString()
        End If
    End Function

    Public Function GetBase10Number() As Double
        If _Base10Number IsNot Nothing Then
            Return _Base10Number
        Else
            Return ToBase10()
        End If
    End Function

    Private Sub TrySetBaseSet(Values As List(Of Char))
        For Each value As Char In _BaseXNumber
            If Not Values.Contains(value) Then
                Throw New ArgumentOutOfRangeException("The string has a value, " & value & ", not contained in the selected 'base' set.")
                _CharacterArray.Clear()
                DetermineNumberBase()
            End If
        Next

        _CharacterArray = Values

    End Sub

    Private Sub TrySetBaseSet(LowValue As Integer, HighValue As Integer)

        Dim HighLow As KeyValuePair(Of Integer, Integer) = GetHighLow()

        If HighLow.Key < LowValue OrElse HighLow.Value > HighValue Then
            Throw New ArgumentOutOfRangeException("The string has a value not contained in the selected 'base' set.")
            _CharacterArray.Clear()
            DetermineNumberBase()
        End If

        NumberBaseLow = LowValue
        NumberBaseHigh = HighValue

    End Sub

    Private Function GetHighLow(Optional Values As List(Of Char) = Nothing) As KeyValuePair(Of Integer, Integer)
        If Values Is Nothing Then
            Values = _BaseXNumber.ToList
        End If

        Dim lowestValue As Integer = Convert.ToInt32(Values(0))
        Dim highestValue As Integer = Convert.ToInt32(Values(0))

        Dim currentValue As Integer

        For Each value As Char In Values

            If value <> DecimalSeparator AndAlso value <> GroupSeparator Then
                currentValue = Convert.ToInt32(value)
                If currentValue > highestValue Then
                    highestValue = currentValue
                End If
                If currentValue < lowestValue Then
                    currentValue = lowestValue
                End If
            End If
        Next

        Return New KeyValuePair(Of Integer, Integer)(lowestValue, highestValue)

    End Function

    Public Sub New(BaseXNumber As String)
        _BaseXNumber = BaseXNumber
        DetermineNumberBase()
    End Sub

    Public Sub New(BaseXNumber As String, NumberBase As Integer)
        Me.New(BaseXNumber, Convert.ToInt32("0"c), NumberBase)
    End Sub

    Public Sub New(BaseXNumber As String, NumberBaseLow As Integer, NumberBaseHigh As Integer)
        _BaseXNumber = BaseXNumber
        Me.NumberBaseLow = NumberBaseLow
        Me.NumberBaseHigh = NumberBaseHigh
    End Sub

    Public Sub New(Base10Number As Double)
        _Base10Number = Base10Number
    End Sub

    Private Sub DetermineNumberBase()
        Dim highestValue As Integer

        Dim currentValue As Integer

        For Each value As Char In _BaseXNumber

            currentValue = Convert.ToInt32(value)
            If currentValue > highestValue Then
                highestValue = currentValue
            End If
        Next

        NumberBaseHigh = highestValue
        NumberBaseLow = Convert.ToInt32("0"c) 'assume 0 is the lowest

    End Sub

    Private Function ToBaseString() As String
        Dim Base10Number As Double = _Base10Number

        Dim intPart As Long = Math.Truncate(Base10Number)
        Dim fracPart As Long = (Base10Number - intPart).ToString.Replace(DecimalSeparator, "")

        Dim intPartString As String = ConvertIntToString(intPart)
        Dim fracPartString As String = If(fracPart <> 0, DecimalSeparator & ConvertIntToString(fracPart), "")

        Return intPartString & fracPartString

    End Function

    Private Function ToBase10() As Double
        Dim intPartString As String = _BaseXNumber.Split(DecimalSeparator)(0).Replace(GroupSeparator, "")
        Dim fracPartString As String = If(_BaseXNumber.Contains(DecimalSeparator), _BaseXNumber.Split(DecimalSeparator)(1), "")

        Dim intPart As Long = ConvertStringToInt(intPartString)
        Dim fracPartNumerator As Long = ConvertStringToInt(fracPartString)
        Dim fracPartDenominator As Long = ConvertStringToInt(GetEncodedChar(1) & String.Join("", Enumerable.Repeat(GetEncodedChar(0), fracPartString.ToString.Length)))

        Return Convert.ToDouble(intPart + fracPartNumerator / fracPartDenominator)

    End Function

    Private Function ConvertIntToString(ValueToConvert As Long) As String
        Dim result As String = String.Empty
        Dim targetBase As Long = GetEncodingCharsLength()

        Do
            result = GetEncodedChar(ValueToConvert Mod targetBase) & result
            ValueToConvert = ValueToConvert \ targetBase
        Loop While ValueToConvert > 0

        Return result
    End Function

    Private Function ConvertStringToInt(ValueToConvert As String) As Long
        Dim result As Long
        Dim targetBase As Integer = GetEncodingCharsLength()
        Dim startBase As Integer = GetEncodingCharsStartBase()

        Dim value As Char
        For x As Integer = 0 To ValueToConvert.Length - 1
            value = ValueToConvert(x)
            result += GetDecodedChar(value) * Convert.ToInt32(Math.Pow(GetEncodingCharsLength, ValueToConvert.Length - (x + 1)))
        Next

        Return result

    End Function

    Private Function GetEncodedChar(index As Integer) As Char
        If _CharacterArray IsNot Nothing AndAlso _CharacterArray.Count > 0 Then
            Return _CharacterArray(index)
        Else
            Return Convert.ToChar(index + NumberBaseLow)
        End If
    End Function

    Private Function GetDecodedChar(character As Char) As Integer
        If _CharacterArray IsNot Nothing AndAlso _CharacterArray.Count > 0 Then
            Return _CharacterArray.IndexOf(character)
        Else
            Return Convert.ToInt32(character) - NumberBaseLow
        End If
    End Function

    Private Function GetEncodingCharsLength() As Integer
        If _CharacterArray IsNot Nothing AndAlso _CharacterArray.Count > 0 Then
            Return _CharacterArray.Count
        Else
            Return NumberBaseHigh - NumberBaseLow + 1
        End If
    End Function

    Private Function GetEncodingCharsStartBase() As Integer
        If _CharacterArray IsNot Nothing AndAlso _CharacterArray.Count > 0 Then
            Return GetHighLow.Key
        Else
            Return NumberBaseLow
        End If
    End Function
End Class

And now for the code to loop through Excel columns:

    Public Function GetColumnList(DataSheetID As String) As List(Of String)
        Dim workingColumn As New BaseNumber("A")
        workingColumn.SetCharacterArray("@ABCDEFGHIJKLMNOPQRSTUVWXYZ")

        Dim listOfPopulatedColumns As New List(Of String)
        Dim countOfEmptyColumns As Integer

        Dim colHasData As Boolean
        Dim cellHasData As Boolean

        Do
            colHasData = True
            cellHasData = False
            For r As Integer = 1 To GetMaxRow(DataSheetID)
                cellHasData = cellHasData Or XLGetCellValue(DataSheetID, workingColumn.GetBaseXNumber & r) <> ""
            Next
            colHasData = colHasData And cellHasData

            'keep trying until we get 4 empty columns in a row
            If colHasData Then
                listOfPopulatedColumns.Add(workingColumn.GetBaseXNumber)
                countOfEmptyColumns = 0
            Else
                countOfEmptyColumns += 1
            End If

            'we are already starting with column A, so increment after we check column A
            Do
                workingColumn.SetNumber(workingColumn.GetBase10Number + 1)
            Loop Until Not workingColumn.GetBaseXNumber.Contains("@")

        Loop Until countOfEmptyColumns > 3

        Return listOfPopulatedColumns

    End Function

You'll note the important part of the Excel part is that 0 is identified by a @ in the re-based number. So I just filter out all the numbers that have an @ in them and I get the proper sequence (A, B, C, ..., Z, AA, AB, AC, ...).


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