Number Systems

    Since there is no real way to express G1 Septendecimal in Visual Studio, we use the String variable type to hold a textual representation of it.  Regardless of the base, there is a general equation for converting it to decimal by calculating each character's base weight and then adding the individual values together.

Public Function AnyToDecimal(ByVal Number As String, ByVal Base As_
	Short) As Long
   Dim lDecimalOutput As Long
   Dim IsNegative As Boolean
   Dim i As Short

   'Lower case a-z may be used to represent something different
   'then their upper case counterparts if desired<
   Number = Number.ToUpper()

   'Roman Numerals (Roman Numerals have no Base technically
   'and are really just an addition problem which needs to be
   'dealt with in a different way)

   If Base = 0 Then
      Return FromRomanNumeral(Number)
   End If

   'Determine if the string is negative
   If Number.StartsWith("-") = True Then
      IsNegative = True
      Number = Number.Replace("-", "")
   End If

   'Remove Invalid Characters
   Dim chrTemp() As Char = Number.ToCharArray

   Number = ""
   For i = 0 To chrTemp.Length - 1
      'Only accept numbers and characters
      If (IsNumber(chrTemp(i).ToString) = True) Or_
             (IsLetter(chrTemp(i).ToString) = True) Then
         Number &= chrTemp(i).ToString
      End If
   Next

   Dim chrNumberSplit() As Char = Number.ToCharArray
   Dim lNumberSplit(chrNumberSplit.GetUpperBound(0)) As Long

   'Supported Bases (1-9 A-Z currently.  This behavior can be_
   'modified to allow "AA" to come after "Z", etc.)
   If Base < 0 Then Throw New Exception("Starting Base must be_
	Greater Than or Equal to 0.")

   'Add the value of each symbol to an array (9 = 9, A = 10,_
   'B = 11, etc.)
   For i = 0 To chrNumberSplit.GetUpperBound(0)
      If Char.IsNumber(chrNumberSplit(i)) Then
         lNumberSplit(i) = Int(chrNumberSplit(i).ToString)
      Else
         'Convert letters to numbers (A = 10, etc.)
         lNumberSplit(i) = Asc(chrNumberSplit(i)) - 55
      End If

      'Checks for "overflow" chacacters (Base 1 is different_
      'because the '1' chacter is used instead of the 0)
      If lNumberSplit(i) > Base - 1 AndAlso Base <> 1 Then
         Throw New Exception(chrNumberSplit(i) & " is not a valid_
	    character in a " & GetBaseName(Base) & " number system.")
      ElseIf Base = 1 AndAlso lNumberSplit(i) <> 1 Then
         Throw New Exception(chrNumberSplit(i) & " is not a valid_
	    character in a " & GetBaseName(Base) & " number system.")
      End If
   Next

   Try
      'Calculate the Base weight of each array item
      For i = 0 To chrNumberSplit.GetUpperBound(0)
         lNumberSplit(i) = lNumberSplit(i) * Base ^_
		(chrNumberSplit.GetUpperBound(0) - i)
      Next

      'Add the weighted values together to produce a Decimal_
      'representation
      For i = 0 To chrNumberSplit.GetUpperBound(0)
         lDecimalOutput += lNumberSplit(i)
      Next

      'If the original number was negative, reflect it
         If IsNegative = True Then
            lDecimalOutput *= -1
      End If
   Catch
      Throw New Exception("[" & Number & "] " & GetBaseName(Base)_
	& " requires more than 64-bits in Decimal form to represent_
	(Overflow).")
   End Try

   Return lDecimalOutput
End Function

The preceding code requires these self explainitry Functions:

Public Function IsNumber(ByVal TestString As String) As Boolean
   Dim chrString() As Char = TestString.ToCharArray
   Dim i0, i9 As Short
   Dim i As Integer

   i0 = Asc("0")
   i9 = Asc("9")

   For i = 0 To TestString.Length - 1  
      If (Asc(chrString(i)) < i0 Or Asc(chrString(i)) > i9) Then
         Return False
         Exit Function
      End If
   Next

   Return True
End Function


Public Function IsLetter(ByVal TestString As String) As Boolean
   Dim chrString() As Char = TestString.ToCharArray
   Dim iLowerA, iLowerZ, iUpperA, iUpperZ As Short
   Dim i As Integer

   iLowerA = Asc("a")
   iLowerZ = Asc("z")
   iUpperA = Asc("A")
   iUpperZ = Asc("Z")

   For i = 0 To TestString.Length - 1
      If (Asc(chrString(i)) >= iLowerA And Asc(chrString(i)) <= iLowerZ)_
	Or (Asc(chrString(i)) >= iUpperA And Asc(chrString(i)) <= iUpperZ) Then
      Else
         Return False
         Exit Function
      End If
   Next

   Return True
End Function