我如何理解此代码挑战中此测试用例的结果？

Question

我正在尝试了解此 challenge 在 codeforces 中的第一个测试用例。

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?

总结

给定一个二进制数，将其十进制值加1，计算运算后改变了多少位？

测试用例

4

1100
= 3

4

1111
= 4

备注在第一个样本中，单元格最终值为 0010，在第二个样本中 - 为 0000.

在2个测试用例中1111是15，所以15+1=16（二进制10000），所以所有1的变化，因此是4

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

Answer 1

你错过了关键部分：最低有效位是第一个（即最左边的），而不是最后一个，因为我们通常写二进制。

因此，1100 不是 12，而是 3。因此，1100 + 1 = 3 + 1 = 4 = 0010，所以 3 位被更改。

"least significant bit"字面上的意思是不是最重要的一点，所以可以理解为"the one representing the smallest value"。在二进制中，表示 2^0 的位是最低位。所以你任务中的二进制代码是这样写的：

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

这就是为什么 1100 是：

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）。

我如何理解此代码挑战中此测试用例的结果？

How can I understand the result of this testcase in this code challenge?

algorithm

bits