algorithm - 我如何理解此代码挑战中此测试用例的结果？

Question

我试图理解这个 challenge 的第一个测试用例在代码力量中。

描述是:

Sergey is testing a next-generation processor. Instead of bytes the processor works with memory cells consisting of n bits. These bits are numbered from 1 to n. An integer is stored in the cell in the following way: the least significant bit is stored in the first bit of the cell, the next significant bit is stored in the second bit, and so on; the most significant bit is stored in the n-th bit. Now Sergey wants to test the following instruction: "add 1 to the value of the cell". As a result of the instruction, the integer that is written in the cell must be increased by one; if some of the most significant bits of the resulting number do not fit into the cell, they must be discarded. Sergey wrote certain values ​​of the bits in the cell and is going to add one to its value. How many bits of the cell will change after the operation?

摘要

给定一个二进制数，将其十进制值加 1，计算运算后有多少位发生变化？

测试用例

4

1100
= 3

4

1111
= 4

注意 在第一个示例中，单元格的最终值为 0010，在第二个示例中，单元格的最终值为 0000。

在2个测试用例中，1111是15，所以15 + 1 = 16(二进制为10000)，所以所有的1都改变了，因此是4

但是在2个测试用例中1100是12，所以12 + 1 = 13(01101)，这里只是最后左边的1改变了，但结果是3，为什么？

Answer 1

您错过了关键部分:最低有效位是第一个(即最左边的)，而不是我们通常编写二进制的最后一个。

因此，1100 不是 12，而是 3。因此，1100 + 1 = 3 + 1 = 4 = 0010，因此更改了 3 位。

“最低有效位”字面意思是不是最高有效位的位，因此您可以将其理解为“代表最小值的位”。在二进制中，表示 2^0 的位是最低有效位。所以你的任务中的二进制代码写成如下:

bit no. 0    1    2    3    4   (...)
value   2^0  2^1  2^2  2^3  2^4 (...)
        | least             | most
        | significant       | significant
        | bit               | bit

这就是 1100 的原因:

1100 = 1 * 2^0 + 1 * 2^1 + 0*2^2 + 0*2^3 = 1 + 2 + 0 + 0 = 3

不是相反(正如我们通常写的那样)。