如何用二进制表示浮点数。电气工程师学会

Question

类似于十进制的二进制数也可以表示浮点数。现在我读到它可以有类似的浮点数

0.5：0.1，0.25：0.01，0.125：0.001...等等。但是，例如，如何用二进制表示0.1（十进制）？

同样，给定一个十进制浮点数，如何将其转换为等效的十进制数（如果不是那么简单的话）。

编辑：所以我知道更好的问题应该是；如何将十进制浮点数转换为二进制？现在我知道我们将小数部分相乘，直到变成零。现在很有可能两个浮点可以具有相同的表示形式吗？

Answer 1

给出多少位？

0.1b：

0.00011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011...

如您所见，这是一个近似值。

Binary                                          Decimal
0.1     == 1/2^1         == 1/2              == 0.5
0.01    == 1/2^2         == 1/4              == 0.25
0.11    == 1/2^1 + 1/2^2 == 1/2 + 1/4 == 3/4 == 0.75

小数点后的每一位代表1/2 ^（position_after_bit_string）。

postion:   |1|2|3|4|5|6|7|
         0.|0|0|0|0|0|0|1|

所以 0.0000001 = 1/2^7 = 0.0078125

伪代码：

decimal_value = 0 
for i, bit in enumerate(binary_string):
    if bit == 1
         decimal_value += 1/2**i

有关更多信息，为什么十进制数字不能完全用二进制表示？