Mathematicaで浮動小数点数を扱う ref: http://qiita.com/butchi_y/items/3c44e94cdac369509bca

file0.txt

In[1]:= ExportString[12345, "Real32"]
Out[1]= ä@F

file3.txt

In[1]: real32Digits[Pi]
In[2]: real32Format[%]
In[3]: fromReal32Digits[%%]
In[4]: N[%]

Out[1]: {0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1,
1, 1, 1, 0, 1, 1, 0, 1, 1}
Out[2]: {1, 1, 13176795/8388608}
Out[3]: 3.14159
Out[4]: 3.14159

file4.txt

In[1]: real32Digits[2^128]
In[2]: real32Format[%]
In[3]: fromReal32Digits[%%]
In[4]: fromReal32DigitsByAbnormal[%%%]

Out[1]: {0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
Out[2]: {1, 128, 1}
Out[3]: Infinity
Out[4]: 340282366920938463463374607431768211456

file5.txt

In[1]: real32Digits[0]
In[2]: real32Format[%]
In[3]: fromReal32Digits[%%]

Out[1]: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
Out[2]: {1, -127, 1}
Out[3]: 0.

file6.txt

nLi = IntegerDigits[First[ImportString[ExportString[-118.625, "Real32"], "UnsignedInteger32"]], 2, 32]
sgnLi = Take[nLi, 1]; (* Sign *)
eLi = Take[nLi, {2, 9}]; (* Exp *)
sLi = Take[nLi, {10, 32}]; (* Mantissa *)
Grid[{Join @@ {Item[#, Background -> LightBlue] & /@ sgnLi, 
    Item[#, Background -> LightGreen] & /@ eLi, 
    Item[#, Background -> LightRed] & /@ sLi}}]

real-32-digits--experiment.nb

In[1] := real32Digits[-118.625]
Out[1] := {1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

In[2]:= real32Format[%]
Out[2] := {-1, 6, 949/512}

In[3] := fromReal32Digits[%%]
Out[3] := -118.625

real-32-digits.nb

(* 数値をIEEE 754 の単精度浮動小数点数表現の01列 （長さ32） に変換 *)
real32Digits[x_] := 
 IntegerDigits[
  First[ImportString[ExportString[x, "Real32"], "UnsignedInteger32"]],
   2, 32]

(* Real32で表された01列から {sgn, e, m} のリストを生成 （特別な数は無視） *)
real32Format[li_] :=
 {If[First[li] === 0, 1, -1],
  FromDigits[Take[li, {2, 9}], 2] - 2^7 + 1,
  FromDigits[{Join[{1}, Take[li, {10, 32}]], 1}, 2]}

(* Real32で表された01列をそれの表す数値に変換 *)
fromReal32Digits[li_] := First[ImportString[ExportString[FromDigits[li, 2], "UnsignedInteger32"], "Real32"]]