Negative representation of a binary number

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I saw online that if you want to convert a binary number to a negative binary number, you add 1.However, I don't understand why you do that.In a forum I saw someone explaining the following:

A little rule that I use when I need to represent negative numbers in binary is
~i = -i-1.
That is, the bitwise inversion of "i" is equivalent to negative "i" less one.
In your example, you're looking for the binary representation of -192. Since -192 = -191-1, the following statement is true:
~191 = -192.

Unfortunately, I don't understand this explanation.I went on further to understand the bit wise inversion of binary and I did understand that: it's only changing 1 into 0 and o into 1. Then I saw the following explanation from Microsoft:

~5 == 11111111 11111111 11111111 11111010 == -6 in decimal.

How do you really get -6 from ~5?How that gives you negative -6. Isn't 6 is 110?And if you add 1 to make it negative, shouldn't it be 111?Can someone please explain?