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浮点数转十进制数

[英]Floating point number to decimal number

原文 2020-10-26 18:19:54 7 1 floating-point/ decimal

I have the following floating point number: 1|011|1001.我有以下浮点数：1|011|1001。 The possible answers in the multiple choice are:多项选择中可能的答案是：
a)-729 a)-729
b)729 b)729
c)72 c)72
d)-72. d)-72。
The answer is d) -72.答案是 d) -72。 But how is it possible?但怎么可能呢？ I have no clue how they calculated this.我不知道他们是如何计算的。 I think my school uses another method than what is known in the internet, because when I try it like in all those tutorials i have seen, it doesn't work.我认为我的学校使用了另一种方法，而不是互联网上已知的方法，因为当我像在我看过的所有教程中一样尝试时，它不起作用。 I even tried it backwards like -72 to floating point but the exponent already would be different.我什至尝试向后像 -72 到浮点数，但指数已经不同了。 Can someone explain ist for me?有人可以为我解释一下吗？

1 个解决方案

In “1|011|1001”, 1 is the sign field, 011 is the exponent field, and 1001 is the significand field.在“1|011|1001”中，1为符号域，011为指数域，1001为有效位域。

The sign bit is 0 for +, 1 for −, so this is −. + 的符号位是 0，- 的符号位是 1，所以这是 -。

011 ₂ is 3, apparently meaning scaling by 2 ³ 011 ₂是 3，显然意味着按 2 ³缩放

1001 ₂ is 9, meaning a significand of 9. 1001 ₂是 9，意思是 9 的有效数。

So the number is − 2 ³ • 9 = −72.所以这个数字是 − 2 ³ • 9 = −72。

However, this is not at all a standard format.但是，这根本不是标准格式。 Usually the exponent is biased (offset) by some value.通常指数会被某个值偏置（偏移）。 This is commonly 2 ^{n −1} −1 for an n -bit field, so the bias would be 3 for a 3-bit field, and 001 would represent an exponent of −2, 010 would represent −1, 011 would represent 0, and so on.对于n位字段，这通常是 2 ^{n -1} -1，因此对于 3 位字段，偏差将为 3，001 表示 -2 的指数，010 表示 -1，011 表示 0，等等。

Additionally, the significand field is usually scaled, so that 1001 would represent .1001 ₂ (9/16) rather than 1001 ₂ (9).此外，有效位字段通常被缩放，因此 1001 将代表 0.1001 ₂ (9/16) 而不是 1001 ₂ (9)。 Also, the significand is usually formed with a leading bit that is 0 or 1 depending on the value of the exponent field.此外，根据指数字段的值，有效数通常由 0 或 1 的前导位构成。

So this format is very different from common formats.所以这种格式与常见的格式有很大的不同。 No test or exercise should expect a student to know it without having documented it previously.任何测试或练习都不应该期望学生在没有事先记录的情况下知道它。