心血來潮地跑到Upworks做了個JavaScript Test，結果當然是慘不忍睹，發現自己對不少JavaScript的基礎知識的理解是模模糊糊，甚至是錯的。

比如這題：

~-(2+"2")

這個表達式的值是21，我腦補了好久也得不到這個答案，這才發現，我完全不理解Bitwise NOT操作符。

不懂就補嘍。

這回還真是“補”，回想起大學那會兒，學到“補碼”時，腦子里就是一團霧，原來那團迷霧到今天也沒散，真他么黏糊。

讀到 Why is ~5 === -6 in JavaScript?：

It does indeed perform a bit-wise NOT, the negative number is in two's complement. So the value 1010 is -6.

Two's complement basically works by the very left-most bit signifies a negative number and is taken as a negative value. All other 1 bits are added to this number. For example:

1010 => (-8 +0 +2 +0) => -6
1111 => (-8 +4 +2 +1) => -1

又琢磨了一會兒，才搞明白為啥補碼這么反直覺。

“二補碼”只能腦補，或者用代碼打印腦補的內容。

在JavaScript里，如果用number.toString(2)，結果是這樣：

Decimal: 5 | Binary: 00000000000000000000000000000101 Decimal: 4 | Binary: 00000000000000000000000000000100 Decimal: 3 | Binary: 00000000000000000000000000000011 Decimal: 2 | Binary: 00000000000000000000000000000010 Decimal: 1 | Binary: 00000000000000000000000000000001 Decimal: 0 | Binary: 00000000000000000000000000000000 Decimal: -0 | Binary: 00000000000000000000000000000000 Decimal: -1 | Binary: 000000000000000000000000000000-1 Decimal: -2 | Binary: 00000000000000000000000000000-10 Decimal: -3 | Binary: 00000000000000000000000000000-11 Decimal: -4 | Binary: 0000000000000000000000000000-100 Decimal: -5 | Binary: 0000000000000000000000000000-101

這個結果符合直覺，但加法器的實現只會使用二補碼，下面是加法器實際使用的“二補碼”：

Decimal: 5 | Binary: 00000000000000000000000000000101 Decimal: 4 | Binary: 00000000000000000000000000000100 Decimal: 3 | Binary: 00000000000000000000000000000011 Decimal: 2 | Binary: 00000000000000000000000000000010 Decimal: 1 | Binary: 00000000000000000000000000000001 Decimal: 0 | Binary: 00000000000000000000000000000000 Decimal: -0 | Binary: 00000000000000000000000000000000 Decimal: -1 | Binary: 11111111111111111111111111111111 Decimal: -2 | Binary: 11111111111111111111111111111110 Decimal: -3 | Binary: 11111111111111111111111111111101 Decimal: -4 | Binary: 11111111111111111111111111111100 Decimal: -5 | Binary: 11111111111111111111111111111011

理解了二補碼，再來看-22怎么被補成21的：

Decimal: -22 | Binary: 11111111111111111111111111101010 -> Decimal: 21 | Binary: 00000000000000000000000000010101

Python對此解釋得更直接：

~ x
Returns the complement of x - the number you get by switching each 1 for a 0 and each 0 for a 1.
This is the same as -x - 1.

我連補碼都沒鬧明白，竟然過了關還Score top 30%，可見其他人都沒作弊，我真是無恥的程序員。

寫了半天，一言以蔽之：

~x 相當于調用

function twosComplement(x){return 0 -x - 1; }

---

參考鏈接：

• Why is ~5 === -6 in JavaScript?
• Why does bitwise “not 1” equal -2?
• MDN Bitwise operators
• Python's bitwise operators.
• Two's Complement

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