将万亿数字转换为二进制

Posted 2023-04-19

【中文标题】将万亿数字转换为二进制

【英文标题】：Convert Trillion number to Binary

【发布时间】：2020-09-11 21:40:47

【问题描述】：

在 VB6 中，我试图将数字转换为二进制，但是当数字有 10 位时，我总是遇到溢出错误。 我可以存储万亿数字的数据类型是什么？ 当号码少于 10 位时，这是有效的代码。

Public Function DecimalToBinary(DecimalNum As Double) As _
String
Dim tmp As String
Dim n As Double

n = DecimalNum

tmp = Trim(Str(n Mod 2))
n = n \ 2

Do While n <> 0
    tmp = Trim(Str(n Mod 2)) & tmp
    n = n \ 2
Loop

DecimalToBinary = tmp
End Function

【问题讨论】：

What is the data type where i can store a trillion number? - docs.microsoft.com/en-us/office/vba/language/reference/…

【参考方案1】：

您将遇到的一个问题是Mod 运算符无法处理大于Long (2,147,483,647) 的值。您可以按照此答案中的描述重写Mod 函数：VBA equivalent to Excel's mod function:

' Divide the number by 2.
' Get the integer quotient for the next iteration.
' Get the remainder for the binary digit.
' Repeat the steps until the quotient is equal to 0.
Public Function DecimalToBinary(DecimalNum As Double) As String
    Dim tmp As String
    Dim n As Double
    
    n = DecimalNum
    
    Do While n <> 0
        tmp = Remainder(n, 2) & tmp
        n = Int(n / 2)
    Loop
    
    DecimalToBinary = tmp

End Function

Function Remainder(Dividend As Variant, Divisor As Variant) As Variant
    Remainder = Dividend - Divisor * Int(Dividend / Divisor)
End Function

你也可以重写你的函数来完全避免Mod：

Public Function DecimalToBinary2(DecimalNum As Double) As String
    Dim tmp As String
    Dim n As Double
    Dim iCounter As Integer
    Dim iBits As Integer
    Dim dblMaxSize As Double
    
    n = DecimalNum
    iBits = 1
    dblMaxSize = 1
    
    ' Get number of bits
    Do While dblMaxSize <= n
        dblMaxSize = dblMaxSize * 2
        iBits = iBits + 1
    Loop

    ' Move back down one bit
    dblMaxSize = dblMaxSize / 2
    iBits = iBits - 1

    ' Work back down bit by bit
    For iCounter = iBits To 1 Step -1
        If n - dblMaxSize >= 0 Then
            tmp = tmp & "1"
            n = n - dblMaxSize
        Else
            ' This bit is too large
            tmp = tmp & "0"
        End If
        dblMaxSize = dblMaxSize / 2
    Next
    
    DecimalToBinary2 = tmp

End Function

此函数查找大于您的数字的位，然后逐位返回，确定是否可以从您的数字中减去每个位的值。这是一种非常基本的方法，但它确实有效。

对于这两个函数，如果您想将二进制字符串分成 8 位组，可以使用这样的函数来填充字符串：

Public Function ConvertToBytes(p_sBits As String)
    Dim iLength As Integer
    Dim iBytes As Integer
    
    iLength = Len(p_sBits)
    If iLength Mod 8 > 0 Then
        iBytes = Int(iLength / 8) + 1
    Else
        iBytes = Int(iLength / 8)
    End If
    
    ConvertToBytes = Right("00000000" & p_sBits, iBytes * 8)

End Function

【讨论】：

你指的是哪个实现？

两个函数都返回相同的字符串。我用随机值测试了这两个值，并将它们与Decimal to Binary Converter 输出进行了比较，它们匹配。

DecimalToBinary2 返回错误的数字。我尝试了3252027161并返回011000001110101111111111100011001和正确的是1100 0001 1101 0101 1111 1111 0001 1001（前面的一个零）和436196801，返回01100111111111110101010111000001和正确的是1 1001 1111 1111 1101 0101 1100 0001 span>

请注意，由于浮点数的精度有限，这对于大于 9,007,199,254,740,990 的整数将失败。 10 位数字不是问题，但未来的读者可能会感兴趣

谢谢@ÉtienneLaneville