可以使用 Convert.ToString 将数字转换为指定基数中的等效字符串表示形式。

例如:

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

然而，正如注释所指出的，Convert.ToString只支持以下有限的——但通常是足够的——基数集: 2、8、10或16。

更新(满足转换到任何基地的要求) :

我不知道在 BCL 中有什么方法可以将数字转换成任何基数，所以你必须编写自己的小实用函数。一个简单的示例应该是这样的(注意，通过替换字符串串联可以更快地实现这一点) :

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);
}
}

更新2(表现改善)

使用数组缓冲区而不是字符串串联来构建结果字符串可以提高性能，特别是在大数量情况下(参见方法 IntToStringFast)。在最好的情况下(即尽可能长的输入) ，这种方法大约快三倍。不过，对于1位数字(即目标基数中的1位数字) ，IntToString会较快。

这个论坛帖子的这门课能帮助你吗？

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;


}


}

完全未经测试... 让我知道如果它的工作! (复制粘贴它，以防论坛帖子消失或其他...)

我使用它将 Guid 存储为一个较短的字符串(但仅限于使用106个字符)。 如果有人感兴趣，这里是我的代码，用于将字符串解码回数值(在本例中，我使用2个乌龙作为 Guid 值，而不是编码一个 Int128(因为我在3.5而不是4.0中)。 为了清楚起见，CODE 是一个包含106个独特字符的字符串 const。

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);
}
}

我也在寻找一种快速的方法，将十进制数转换为[2]范围内的另一个基数。所以我开发了以下代码。遵循它很简单，并且使用 StringBuilder 对象作为字符缓冲区的代理，我们可以逐字符索引字符。与替代方案相比，该代码似乎非常快，而且比在字符数组中初始化单个字符要快得多。

对于你自己的用途，你可能更喜欢: 1/返回空字符串而不是抛出异常。 2/删除基数检查，使方法运行得更快 3/用32’0初始化 StringBuilder 对象并删除行结果。删除(0，i) ; 。这将导致字符串以前导零返回，并进一步提高速度。 4/使 StringBuilder 对象成为类中的静态字段，因此无论 DecimalToBase 方法被调用多少次，StringBuilder 对象只初始化一次。如果你做了这个改变，上面的3将不再起作用。

我希望有人会觉得这很有用:)

原子悖论

        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());
}

我也有类似的需求，除了我还需要对“数字”做数学运算。我在这里采纳了一些建议，并创建了一个类，将做所有这些有趣的东西。它允许任何 Unicode字符被用来表示一个数字，它也适用于小数。

这个类很容易使用。只需创建一个类型为 New BaseNumber的数字，设置一些属性，然后关闭。这些例程会自动在基数10和基数 x 之间切换，你设置的值保留在你设置的基数中，所以不会丢失精度(直到转换，但即使那样，精度损失应该是非常小的，因为这个例程在任何可能的地方使用 Double和 Long)。

我不能指挥这支舞的速度。它可能相当慢，所以我不确定它是否适合提出问题的人的需要，但它肯定是灵活的，所以希望其他人可以使用它。

对于可能需要此代码来计算 Excel 中下一列的任何其他人，我将包含利用此类的循环代码。

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

现在开始循环 Excel 列的代码:

    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

您将注意到 Excel 部分的重要部分是，0在基于 re 的数字中由一个@标识。所以我只需要过滤掉所有包含@的数字，然后得到正确的序列(A，B，C，... ，Z，AA，AB，AC，...)。

我最近在博客上写到了这一点。在计算过程中，我的实现没有使用任何字符串运算，这使得它成为 非常快。支持转换为以2为基数的任何数字系统到36:

/// <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;
}