IEEE 754中有多少个整数 [英] how many whole numbers in IEEE 754

问题描述

我试图找出在ieee 754中存在多少个不同的整数。我得到的数字是1778384895，但我找不到任何资源来检查我自己。
非常感谢。

解决方案

我会假设单精度浮点数。

我们得到了零，虽然可以表示为负零，但仍然只是零作​​为一个整数，所以我把它算为一个。

指数小于127的数字不是整数。

 指数空位＃数字
 127 0 1 
 128 1 2 
 129 2 4 
 ... 
 149 22 2 ^ 22 
  

这些总和为 2 ^ 23-1 。如果指数大于149，所有的数字都是整数。所以这是一个额外的 105 * 2 ^ 23 数字（指数255是保留的）。所有这些都是正面的和负面的。

总计是

pre $ 1 +（（2 ^ 23-1）+ 105 *（2 ^ 23））* 2 = 1778384895


所以看起来你是对的。很好的问题，乍看起来很容易：）

I am trying to figure out how many different whole numbers exist in the ieee 754. The number I got was 1778384895 but I couldn't find any resource to check myself. Thanks a lot in advance.

解决方案

I will assume single precision floats.

We got the zero, which although can be represented as negative zero, is still just zero as an integer so I count it as one.

Numbers with exponent less than 127 are not integers.

Exponent   Free bits   # Numbers
127        0           1
128        1           2
129        2           4
...
149        22          2^22

These sum up to 2^23-1. If exponent is greater than 149, all the numbers are integers. So that's an additional 105*2^23 numbers (exponent 255 is reserved). All of these come in positive and negative.

The grand total is thus

1 + ((2^23 - 1) + 105 * (2^23)) * 2 = 1778384895

So looks like you were right. Nice question, it looked a lot easier at first sight :)

这篇关于IEEE 754中有多少个整数的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！