#include <String.au3>
#include <Array.au3>
#cs
0.125 0000003e
12.25 00004441
-0.125 000000be
1.3 6666a63f 1.299999952316284
0.3125 0000a030
0.2 c8cc4c3e 0.199999928474426
0.3 9899993e 0.299999952316284
#ce

Local $aArray = StringSplit("0.125,12.25,-0.125,1.3,0.3125,0.2,0.3", ",")
For $i = 1 To UBound($aArray)-1
ConsoleWrite(@LF&‘----------------------------------------‘&@LF&@LF)
Local $floatHex=FloatToHex($aArray[$i])
ConsoleWrite(‘=>‘ &$floatHex& @LF)
ConsoleWrite(@LF)
BinaryToFloat($floatHex)

Next

;1位符號位+8位指數+23位尾數
Func FloatToHex($floatStr)
;符號位 正數為0 負數為1
Local $pegativeStr = ‘0‘
If StringInStr($floatStr, "-") <> 0 Then $pegativeStr = ‘1‘
Local $pos = StringInStr($floatStr, ".")
;小數點左邊的值
Local $left = StringLeft($floatStr, $pos - 1)
;小數點右邊的值
Local $right = StringRight($floatStr, StringLen($floatStr) - StringLen($left) - 1)
Local $binaryStr = DecimalToBinary(Number($left)) & FloatSmailDecimalToBinary(Number(‘0.‘ & $right, 3))
ConsoleWrite($floatStr & ‘=>‘ & $binaryStr & @LF)
;二進制串中，從左邊算起第一個數字1的位置 例 1100.01 值為1
Local $leftOnePos = StringInStr($binaryStr, "1", 0, 1);
;二進制串中，小數點的位置 例 1100.01 值為5
Local $decimalPos = StringInStr($binaryStr, ".");
;指數部分為二進制浮點數正規化後，小數點移動的位數+127
;0.0011 2-5=-3 1001.01 5-1=4移動次數需再減1
Local $exponent = $decimalPos - $leftOnePos + 127
If ($decimalPos - $leftOnePos) > 0 Then $exponent -= 1
Local $exponentBinaryStr = DecimalToBinary($exponent)
ConsoleWrite(‘Exponent=>‘ & $exponent)
;指數左邊補足8位
$exponentBinaryStr = _StringRepeat("0", 8 - StringLen($exponentBinaryStr)) & $exponentBinaryStr
ConsoleWrite(‘=>‘ & $exponentBinaryStr & @LF)
;尾數部分
Local $tailBinaryStr = StringReplace(StringMid($binaryStr, $leftOnePos + 1), ‘.‘, "")
;用0補足23位
$tailBinaryStr &= _StringRepeat("0", 23 - StringLen($tailBinaryStr))
ConsoleWrite(‘Tail=>‘ & $tailBinaryStr & @LF)
Local $floatBinaryStr = $pegativeStr & $exponentBinaryStr & $tailBinaryStr;
ConsoleWrite(‘=>‘ & $pegativeStr & ‘ ‘ & $exponentBinaryStr & ‘ ‘ & $tailBinaryStr & @LF)
Local $result = ‘‘
For $i = 0 To StringLen($floatBinaryStr) / 4 - 1 Step 1
$result &= DecimalToHex(BinaryToDecimal(StringMid($floatBinaryStr, $i * 4 + 1, 4)))
Next
Return StringLower(MemData($result))
EndFunc ;==>FloatToBinary

Func BinaryToFloat($hexStr)
Local $binaryStr = HexToBinary(MemData($hexStr))
ConsoleWrite($hexStr & ‘=>‘ & $binaryStr & @LF)
Local $pegativeStr = ‘‘;
If StringLeft($binaryStr, 1) = ‘1‘ Then $pegativeStr = ‘-‘
Local $exponentBinaryStr = StringMid($binaryStr, 2, 8)
ConsoleWrite(‘ExponentBinary=>‘ & $exponentBinaryStr & @LF)
Local $tailBinaryStr = StringMid($binaryStr, 10, 23)
ConsoleWrite(‘TailBinary=>‘ & $tailBinaryStr & @LF)
Local $exponent = BinaryToDecimal($exponentBinaryStr) - 127
ConsoleWrite(‘Exponent=>‘ & $exponent & @LF)
Local $tail = "1." & $tailBinaryStr
Local $newTail = ‘‘
If $exponent >= 0 Then
$newTail = StringReplace(StringLeft($tail, $exponent + 2), ".", "") & ‘.‘ & StringMid($tail, $exponent + 3)
Else
$newTail = ‘0.‘ & _StringRepeat("0", -$exponent - 1) & StringReplace($tail, ‘.‘, ‘‘)
EndIf
ConsoleWrite(‘Tail=>‘ & $newTail & @LF)
Local $decimalPos = StringInStr($newTail, ".");
Local $result = BinaryToDecimal(StringLeft($newTail, $decimalPos - 1)) & BinaryToSmailDecimal(StringMid($newTail, $decimalPos + 1))
ConsoleWrite(‘=>‘ & $result & @LF)
Return $pegativeStr & $result
EndFunc ;==>BinaryToFloat

Func MemData($hexStr)
Local $result = ‘‘
Local $index = StringLen($hexStr) / 2 - 1
For $i = $index To 0 Step -1
$result &= StringMid($hexStr, $i * 2 + 1, 2)
Next
Return $result
EndFunc ;==>MemData

#cs
如0.638
1、將其乘二：0.638*2=1.276 則二進制小數的二分位是1.276整數部分1
2、取小數0.276，0.276*2=0.552 則二進制小數的二十分位是0.522整數部分0
3、重復1
得：（0.638）10=（約等於）（0.1010）2
#ce
;小數部分轉二進制
Func FloatSmailDecimalToBinary($float)
Local $floatStr = String($float)
Local $leftChar = ‘‘
Local $result = ‘‘
For $i = 1 To 23 Step 1
$float = $float * 2
If ($float = 0) Then ExitLoop ;
$floatStr = String($float)
$leftChar = StringLeft($floatStr, 1)
$result &= $leftChar
$temp = StringFormat(‘%f‘, ‘0.‘ & StringMid($floatStr, 3, StringLen($floatStr) - 2))
$float = $temp;
Next
Return ‘.‘ & $result
EndFunc ;==>FloatSmailDecimalToBinary

;十進制轉二進制
Func DecimalToBinary($dec)
Local $temp = 0, $shit = 0
For $a = 1 To BinaryLen($dec) * 8 Step 1
$shit = $a
If (2 ^ $a > $dec) Then ExitLoop
Next
Local $result = ""
For $i = 0 To $shit - 1 Step 1
$result &= Chr(BitAND(0x1, BitShift($dec, $i)) + Asc("0"))
Next
Return _StringReverse($result)
EndFunc ;==>DecimalToBinary

;二進制轉十進制
Func BinaryToDecimal($bin)
Local $result = 0
Local $binArray = StringSplit($bin, "", 2)
For $a = UBound($binArray) To 1 Step -1
Local $number = StringMid($bin, $a, 1)
If $number = "1" Then
$result += 2 ^ (UBound($binArray) - $a)
EndIf
Next
Return $result
EndFunc ;==>BinaryToDecimal

;二進制小數轉十進制
Func BinaryToSmailDecimal($bin)
Local $result = 0
Local $binArray = StringSplit($bin, "", 2)
For $a = 1 To UBound($binArray) Step 1
Local $number = StringMid($bin, $a, 1)
If $number = "1" Then
$result += 2 ^ - $a
EndIf
Next
Return StringMid($result, 2)
EndFunc ;==>BinaryToSmailDecimal

;十進制轉十六進制
Func DecimalToHex($dec)
Local $temp = 0, $shit = 0
Local $hexChar = ‘0123456789ABCDEF‘
Local $hexCharArray = StringSplit($hexChar, ‘‘, 2)
For $a = 1 To BinaryLen($dec) * 8 Step 1
$shit = $a
If (16 ^ $a > $dec) Then ExitLoop
Next
Local $result = ""
For $i = 0 To $shit - 1 Step 1
$dddd = BitAND(0xf, BitShift($dec, $i * 4))
$result &= $hexCharArray[$dddd]
Next
Return _StringReverse($result)
EndFunc ;==>DecimalToHex

;十六進制轉二進制
Func HexToBinary($hex)
If StringUpper(StringLeft($hex, 2)) = "0x" Then $hex = StringUpper(StringRight($hex, StringLen($hex) - 2))
Local $bits = "0000|0001|0010|0011|0100|0101|0110|0111|1000|1001|1010|1011|1100|1101|1110|1111"
$bits = StringSplit($bits, ‘|‘, 2)
Local $hexInputArray = StringSplit($hex, ‘‘, 2)
Local $result = ""
For $a In $hexInputArray
$result &= $bits[Dec($a)]
Next
Return $result
EndFunc ;==>HexToBinary

運行結果：

--------------------------------------------------------------------------------

0.125=>0.001
Exponent=>124=>01111100
Tail=>00000000000000000000000
=>0 01111100 00000000000000000000000
=>0000003e

0000003e=>00111110000000000000000000000000
ExponentBinary=>01111100
TailBinary=>00000000000000000000000
Exponent=>-3
Tail=>0.00100000000000000000000000
=>0.125

--------------------------------------------------------------------------------

12.25=>1100.01
Exponent=>130=>10000010
Tail=>10001000000000000000000
=>0 10000010 10001000000000000000000
=>00004441

00004441=>01000001010001000000000000000000
ExponentBinary=>10000010
TailBinary=>10001000000000000000000
Exponent=>3
Tail=>1100.01000000000000000000
=>12.25

--------------------------------------------------------------------------------

-0.125=>0.001
Exponent=>124=>01111100
Tail=>00000000000000000000000
=>1 01111100 00000000000000000000000
=>000000be

000000be=>10111110000000000000000000000000
ExponentBinary=>01111100
TailBinary=>00000000000000000000000
Exponent=>-3
Tail=>0.00100000000000000000000000
=>0.125

--------------------------------------------------------------------------------

1.3=>1.01001100110011001100110
Exponent=>127=>01111111
Tail=>01001100110011001100110
=>0 01111111 01001100110011001100110
=>6666a63f

6666a63f=>00111111101001100110011001100110
ExponentBinary=>01111111
TailBinary=>01001100110011001100110
Exponent=>0
Tail=>1.01001100110011001100110
=>1.299999952316284

--------------------------------------------------------------------------------

0.3125=>0.0101
Exponent=>125=>01111101
Tail=>01000000000000000000000
=>0 01111101 01000000000000000000000
=>0000a03e

0000a03e=>00111110101000000000000000000000
ExponentBinary=>01111101
TailBinary=>01000000000000000000000
Exponent=>-2
Tail=>0.0101000000000000000000000
=>0.3125

--------------------------------------------------------------------------------

0.2=>0.00110011001100110011001
Exponent=>124=>01111100
Tail=>10011001100110011001000
=>0 01111100 10011001100110011001000
=>c8cc4c3e

c8cc4c3e=>00111110010011001100110011001000
ExponentBinary=>01111100
TailBinary=>10011001100110011001000
Exponent=>-3
Tail=>0.00110011001100110011001000
=>0.199999928474426

--------------------------------------------------------------------------------

0.3=>0.01001100110011001100110
Exponent=>125=>01111101
Tail=>00110011001100110011000
=>0 01111101 00110011001100110011000
=>9899993e

9899993e=>00111110100110011001100110011000
ExponentBinary=>01111101
TailBinary=>00110011001100110011000
Exponent=>-2
Tail=>0.0100110011001100110011000
=>0.299999952316284

Float浮點數轉二進制串和十六進制串