一、概述

正整数直接按照源码存储，负整数按照补码存储，那么小数如何存储表示?

二、浮点数的概念(IEEE754)

浮点数是计算机中用于表示实数的一种方法,类似于科学计数法，如:

• 314.4=3.144x10²
• 0.00314=3.14x10^-3
• 255=2.55x10²
  由于电脑存储2进制长度有限,这种方法仅能近似的表示某个数。
  Java中存放浮点数遵守的标准是IEEE754。

三、IEEE754标准

其定义如何用2进制来存储浮点数,根据公式:
V=(-1)^N x M x 2^R
其中:

• N=为符号位,N=1，则为负数;N=0，则为整数
• M=底数(尾数)
• R=幂(指数)
  三部分(NMR)分开存储,有两种方案。

(一)、单精度(32位)

? 1(符号位)+8(指数)+23(底数)，N-(R+127)-M
![][1]

(二)、双精度(64位)

1(符号位)+11(指数)+52(底数)，N-(R+1023)-M
![][2]

(三)、特殊值

• 无穷 : 指数全为1,底数全为0

0 11111111 000000000000....0000
1 11111111 000000000000....0000

• NaN(not a number) : 指数全为1,底数不全为0

0 1111111 101010010...0000
1 1111111 101010000...0000

四、如何存储(如3.14)

(一)、把小数转换为2进制

3.14=0b11.0010001111010111...

(二)、转换为公式格式,底数部分小数点前为1

V=(-1)^N x M x 2^R
0b11.0010001111010111...
=(-1)⁰ x 1.10010001111010111... x 2¹

(三)、符号位N计算

正数为0,负数为1
3.14为正,N=0

(四)、指数部分R计算

R=1
指数部分R要加上127,转换为2进制(无符号)
指数1 加上127(1+127)=128
=0b1000 0000
R=0b1000 0000

(五)、底数部分M计算

去掉小数点前面的1,把剩余的序列拼接即可(如何位数超过范围,会进行四舍五入)
1.10010001111010111...=(丢掉1,这样可以多表示一位数)
M=10010001111010111...

(六)、6)组合起来

3.14=N-R-M
3.14=0b0_10000000_10010001111010111000011

五、总结

1. 浮点数不能准确表示小数
2. 单精度最大值约是3.40E38,最小值(1.40E-45)
3. 双精度最大值约是1.79E308,最小值(4.94E-324)
4. 浮点数如何存储了解即可
   [1]:data:image/png;base64,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
   [2]: data:image/png;base64,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