CODEWITHSUNDEEP
pythonbit-manipulation
David Cardozo
David Cardozo

Reputation: 123

Doing bitwise complement on a 16-bit signal (Python) operator ^

Small question, I'm trying to do the bitwise complement (NOT) of a signal that is 16-bit long. In Python from the documentation, I naively thought that doing the following would work:

~ x

To my surprise this returns negative numbers. I asked in a chat and they told me to use:

x ^ 65535

The thing that I still do not understand is why this works.

Why does this work?

Upvotes: 0

Views: 1178

Answers (1)

Anders
Anders

Reputation: 2316

~x inverts all the bits of x including its sign bit. x ^ 65535 inverts just the lower 16-bits of x.

The ^ means bitwise XOR operation. The truth table for single bit a XOR b is:

a b | a^b
---------
0 0 | 0
0 1 | 1    <-
1 0 | 1
1 1 | 0    <-

XOR has an interesting property that a ^ 0 = a (identity) and a ^ 1 = not a (invert). You can see this in the <- lines in the above table.

So what x ^ 65535 (or x ^ 0xffff which is clearer) does is bitwise XOR the lower 16 bits with 16 ones to invert just the lower 16 bits (0xffff == 65535 is 16 ones). So for a 32 bit example:

       xxxx xxxx xxxx xxxx aaaa aaaa aaaa aaaa
xor    0000 0000 0000 0000 1111 1111 1111 1111
----------------------------------------------
       xxxx xxxx xxxx xxxx AAAA AAAA AAAA AAAA (where A is ~a)

The x's represent bits that remain the same in the input and result. The A's represent bits that have been inverted.

BTW: another way to do the same thing would have been:

~x & 0xffff

Upvotes: 6

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