数字0在二进制浮点格式中看起来如何？ [英] How does the number 0 look like in binary float format?

问题描述

浮点格式（IEEE）有32位。在符号的第一位之后，有8位用于偏置指数，之后是23位用于尾数。在这个尾数是第一个1（总是1）总是隐藏，这导致我的问题：

数字0如何在这种格式？因为如果指数0的数字总是1.
加尾数永远是最小的1右？如果他们在尾数只有零，它会计为'1.0'...

我真的不明白这一点。

解决方案

Wikipedia

a>告诉你：

  0000 0000 = 0 
 8000 0000 = -0 
 次正常数字;其中2 ^ -127以下的数字近似为固定的，而不是浮点型指数。
 
 
实际上，零是一个正常次正规数。子异常以（ -  1）signbits×2 ^ -126×0.significandbits 和指数全零编码。如果有效位为零，则结果为（+/-）零。
 
The float format (IEEE) has 32 bits. First bit for the sign, after that 8 bits for a biased exponent and after that another 23 bits for the mantissa. In this mantissa is the first 1 (is always 1) always hidden which leads me to my question:

how does the number 0 look like in this format? because if the exponents 0 the number will always be 1.
plus the mantissa is always minimum 1 right? If they are only zeros in the mantissa it will count as '1.0'...

I really don't get this.
解决方案
Wikipedia tells you:
0000 0000   = 0
8000 0000   = −0
Besides the normal float values, with exponent and mantisse there are a bunch of other irregular numbers like zero, infinity and a bunch of NaNs. There are also subnormal numbers; where numbers below 2^-127 are approximated with fixed instead of a floating exponent.

Actually, zero is a normal subnormal number. Subnormals are encoded with as (−1)signbits×2^−126 × 0.significandbits and exponent all zero. If significantbits is zero, the result is (+/-) zero.

                        
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