2的补重馏分presentation？ [英] 2's complement representation of fractions?

问题描述

我有点失去了对这个。我需要使用两个小数位
0（A-1）（A-2）

I'm a little lost on this. I need to use two fractional bits 0.(a-1)(a-2)

这样，现在我可以使用 .00 0.01 0.10 和 0.11
但我需要负数（2的补数）也，故将 0.10 是 - 5 ？或者会是 - 25 ？
同样与 0.11 ，这将是 - 75 ？或者会是 - 5 ？
我是pretty肯定它会在两种情况下前者，但我不能完全肯定的。

Like that, now I can use .00 .01 .10 and .11 But I need negative numbers (in 2's complement) also, so would .10 be -.5 ? or would it be -.25 ? The same with .11 , that would be -.75? or would it be -.5 ? I'm pretty sure it would be the former in both cases, but I'm not entirely positive.

推荐答案

在二进制补码，全部设置为1负数的最显著位让我们假设你存储这些数值为8位， 2向右侧的二进制小数点。

In two's complement notation, all of the most significant bits of a negative number are set to 1. Let's assume you're storing these numbers as 8 bits, with 2 to the right of the "binary point."

根据定义， X + -x = 0 ，所以我们可以这样写：

By definition, x + -x = 0, so we can write:

0.5  +  -0.5 = 0.10 + 111111.10 = 0   // -0.5  = 111111.10
0.25 + -0.25 = 0.01 + 111111.11 = 0   // -0.25 = 111111.11
0.75 + -0.75 = 0.11 + 111111.01 = 0   // -0.75 = 111111.01

等。

使用8位这样，你可以存储数量最多

Using 8 bits like this, the largest number you can store is

011111.11 = 31.75

的最小正数是

the least-positive number is

000000.01 = 0.25

的至少负数是

the least-negative number is

111111.11 = -0.25

和最小（即，最负）是

100000.00 = -32

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