JavaScript Bitwise NOT Operator

心血來潮地跑到Upworks作了個JavaScript Test，結果固然是慘不忍睹，發現本身對很多JavaScript的基礎知識的理解是模模糊糊，甚至是錯的。

好比這題：

~-(2+"2")

這個表達式的值是21，我腦補了很久也得不到這個答案，這才發現，我徹底不理解Bitwise NOT操做符。

不懂就補嘍。

這回還真是「補」，回想起大學那會兒，學到「補碼」時，腦子裏就是一團霧，原來那團迷霧到今天也沒散，真他麼黏糊。

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

又琢磨了一下子，才搞明白爲啥補碼這麼反直覺。

「二補碼」只能腦補，或者用代碼打印腦補的內容。

在JavaScript裏，若是用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怎麼被補成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，居然過了關還Score top 30%，可見其餘人都沒做弊，我真是無恥的程序員。

寫了半天，一言以蔽之：

~x 至關於調用

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

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參考連接：

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