作業系統 ： CentOS7.3.1611_x64
gcc版本 ：4.8.5
基本存儲格式（從高到低） ： Sign + Exponent + Fraction
Sign ： 符号位
Exponent ： 階碼
Fraction ： 有效數字
32位浮點數存儲格式解析
Sign ： 1 bit（第31個bit）
Exponent ：8 bits （第 30 至 23 共 8 個bits）
Fraction ：23 bits （第 22 至 0 共 23 個bits）
32位非0浮點數的真值為(python文法) ：
(-1) **Sign * 2 **(Exponent-127) * (1 + Fraction) 示例如下：
a = 12.5
1、求解符号位
a大于0，則 Sign 為 0 ，用二進制表示為： 0
2、求解階碼
a表示為二進制為： 1100.0
小數點需要向左移動3位，則 Exponent 為 130 （127 + 3），用二進制表示為： 10000010
3、求解有效數字
有效數字需要去掉最高位隐含的1，則有效數字的整數部分為 ： 100
将十進制的小數轉換為二進制的小數的方法為将小數*2，取整數部分，則小數部分為： 1
後面補0，則a的二進制可表示為： 01000001010010000000000000000000
即 ： 0100 0001 0100 1000 0000 0000 0000 0000
用16進制表示 ： 0x41480000
4、還原真值
Sign = bin(0) = 0
Exponent = bin(10000010) = 130
Fraction = bin(0.1001) = 2 ** (-1) + 2 ** (-4) = 0.5625 真值：
(-1) **0 * 2 **(130-127) * (1 + 0.5625) = 12.5 32位浮點數二進制存儲解析代碼（c++）：
https://github.com/mike-zhang/cppExamples/blob/master/dataTypeOpt/IEEE754Relate/floatTest1.cpp
運作效果：
[root@localhost floatTest1]# ./floatToBin1
sizeof(float) : 4
sizeof(int) : 4
a = 12.500000
showFloat : 0x 41 48 00 00
UFP : 0,82,480000
b : 0x41480000
showIEEE754 a = 12.500000
showIEEE754 varTmp = 0x00c00000
showIEEE754 c = 0x00400000
showIEEE754 i = 19 , a1 = 1.000000 , showIEEE754 c = 00480000 , showIEEE754 b = 0x41000000
showIEEE754 i = 18 , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = 17 , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = 16 , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = 15 , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = 14 , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = 13 , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = 12 , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = 11 , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = 10 , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = 9 , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = 8 , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = 7 , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = 6 , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = 5 , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = 4 , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = 3 , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = 2 , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = 1 , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 : 0x41480000
[root@localhost floatTest1]# 64位浮點數存儲格式解析
Sign ： 1 bit（第31個bit）
Exponent ：11 bits （第 62 至 52 共 11 個bits）
Fraction ：52 bits （第 51 至 0 共 52 個bits）
64位非0浮點數的真值為(python文法) ：
(-1) **Sign * 2 **(Exponent-1023) * (1 + Fraction) 示例如下：
a = 12.5
1、求解符号位
a大于0，則 Sign 為 0 ，用二進制表示為： 0
2、求解階碼
a表示為二進制為： 1100.0
小數點需要向左移動3位，則 Exponent 為 1026 （1023 + 3），用二進制表示為： 10000000010
3、求解有效數字
有效數字需要去掉最高位隐含的1，則有效數字的整數部分為 ： 100
将十進制的小數轉換為二進制的小數的方法為将小數*2，取整數部分，則小數部分為： 1
後面補0，則a的二進制可表示為：
0100000000101001000000000000000000000000000000000000000000000000
即 ： 0100 0000 0010 1001 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000
用16進制表示 ： 0x4029000000000000
4、還原真值
Sign = bin(0) = 0
Exponent = bin(10000000010) = 1026
Fraction = bin(0.1001) = 2 ** (-1) + 2 ** (-4) = 0.5625 真值：
(-1) **0 * 2 **(1026-1023) * (1 + 0.5625) = 12.5 64位浮點數二進制存儲解析代碼（c++）：
https://github.com/mike-zhang/cppExamples/blob/master/dataTypeOpt/IEEE754Relate/doubleTest1.cpp
運作效果：
[root@localhost t1]# ./doubleToBin1
sizeof(double) : 8
sizeof(long) : 8
a = 12.500000
showDouble : 0x 40 29 00 00 00 00 00 00
UFP : 0,402,0
b : 0x0
showIEEE754 a = 12.500000
showIEEE754 logLen = 3
showIEEE754 c = 4620693217682128896(0x4020000000000000)
showIEEE754 b = 0x4020000000000000
showIEEE754 varTmp = 0x8000000000000
showIEEE754 c = 0x8000000000000
showIEEE754 i = 48 , a1 = 1.000000 , showIEEE754 c = 9000000000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 47 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 46 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 45 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 44 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 43 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 42 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 41 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 40 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 39 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 38 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 37 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 36 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 35 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 34 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 33 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 32 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 31 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 30 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 29 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 28 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 27 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 26 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 25 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 24 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 23 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 22 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 21 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 20 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 19 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 18 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 17 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 16 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 15 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 14 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 13 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 12 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 11 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 10 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 9 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 8 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 7 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 6 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 5 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 4 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 3 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 2 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = 1 , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 : 0x4029000000000000
[root@localhost t1]# 好，就這些了，希望對你有幫助。
本文github位址：
https://github.com/mike-zhang/mikeBlogEssays/blob/master/2018/20180117_IEEE754标準的浮點數存儲格式.rst
歡迎補充
