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IEEE754标准的浮点数存储格式

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09/03
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操作系统 ： CentOS7.3.1611_x64

gcc版本 ：4.8.5

基本存储格式（从高到低） ： Sign + Exponent + Fraction

Sign ： 符号位

Exponent ： 阶码

Fraction ： 有效数字

32位浮点数存储格式解析

Sign ： 1 bit（第31个bit）

Exponent ：8 bits （第 30 至 23 共 8 个bits）

Fraction ：23 bits （第 22 至 0 共 23 个bits）

32位非0浮点数的真值为(python语法) ：

(-1) **Sign * 2 **(Exponent-127) * (1 + Fraction)

示例如下：

a = 12.5

1、求解符号位

a大于0，则 Sign 为 0 ，用二进制表示为： 0

2、求解阶码

a表示为二进制为： 1100.0

小数点需要向左移动3位，则 Exponent 为 130 （127 + 3），用二进制表示为： 10000010

3、求解有效数字

有效数字需要去掉最高位隐含的1，则有效数字的整数部分为 ： 100

将十进制的小数转换为二进制的小数的方法为将小数*2，取整数部分，则小数部分为： 1

后面补0，则a的二进制可表示为： 01000001010010000000000000000000

即 ： 0100 0001 0100 1000 0000 0000 0000 0000

用16进制表示 ： 0x41480000

4、还原真值

Sign = bin() = Exponent = bin() = Fraction = bin(0.1001) = ** (-) + ** (-) = 0.5625

真值：

(-) ** * **(-) * ( + 0.5625) = 12.5

32位浮点数二进制存储解析代码（c++）：

https://github.com/mike-zhang/cppExamples/blob/master/dataTypeOpt/IEEE754Relate/floatTest1.cpp

运行效果：

[root@localhost floatTest1]# ./floatToBin1
sizeof(float) :
sizeof(int) :
a = 12.500000
showFloat : 0x
UFP : ,,
b : 0x41480000
showIEEE754 a = 12.500000
showIEEE754 varTmp = 0x00c00000
showIEEE754 c = 0x00400000
showIEEE754 i = , a1 = 1.000000 , showIEEE754 c = , showIEEE754 b = 0x41000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x41000000
showIEEE754 : 0x41480000
[root@localhost floatTest1]#

64位浮点数存储格式解析

Sign ： 1 bit（第31个bit）

Exponent ：11 bits （第 62 至 52 共 11 个bits）

Fraction ：52 bits （第 51 至 0 共 52 个bits）

64位非0浮点数的真值为(python语法) ：

(-) **Sign * **(Exponent-) * ( + Fraction)

示例如下：

a = 12.5

1、求解符号位

a大于0，则 Sign 为 0 ，用二进制表示为： 0

2、求解阶码

a表示为二进制为： 1100.0

小数点需要向左移动3位，则 Exponent 为 1026 （1023 + 3），用二进制表示为： 10000000010

3、求解有效数字

有效数字需要去掉最高位隐含的1，则有效数字的整数部分为 ： 100

将十进制的小数转换为二进制的小数的方法为将小数*2，取整数部分，则小数部分为： 1

后面补0，则a的二进制可表示为：

0100000000101001000000000000000000000000000000000000000000000000

即 ： 0100 0000 0010 1001 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000

用16进制表示 ： 0x4029000000000000

4、还原真值

Sign = bin() =
Exponent = bin() =
Fraction = bin(0.1001) = ** (-) + ** (-) = 0.5625

真值：

(-) ** * **(-) * ( + 0.5625) = 12.5

64位浮点数二进制存储解析代码（c++）：

https://github.com/mike-zhang/cppExamples/blob/master/dataTypeOpt/IEEE754Relate/doubleTest1.cpp

运行效果：

[root@localhost t1]# ./doubleToBin1
sizeof(double) :
sizeof(long) :
a = 12.500000
showDouble : 0x
UFP : ,,
b : 0x0
showIEEE754 a = 12.500000
showIEEE754 logLen =
showIEEE754 c = (0x4020000000000000)
showIEEE754 b = 0x4020000000000000
showIEEE754 varTmp = 0x8000000000000
showIEEE754 c = 0x8000000000000
showIEEE754 i = , a1 = 1.000000 , showIEEE754 c = , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 i = , a1 = 0.000000 , showIEEE754 b = 0x4020000000000000
showIEEE754 : 0x4029000000000000
[root@localhost t1]#

好，就这些了，希望对你有帮助。

本文github地址：

https://github.com/mike-zhang/mikeBlogEssays/blob/master/2018/20180117_IEEE754标准的浮点数存储格式.rst

欢迎补充