What is bit-by-bit operation?

Question

I've read a few things here in Stack Overflow, but I didn't quite get it.

For example, in context:

Considering the bit-by-bit operation 15^3, the result will be:

0

bit

Author: Woss, 2018-07-16

Source

1 answers

score 6 · Accepted Answer

The question is: what does 15 ^ 3 or 15 xor 3 mean bit by bit?

First we convert 15 and 3 of the decimal base to binary base:

15 : 1111
 3 : 0011

How does XOR work?

XOR or or Exclusive is true if bits A B are different and false if they are equal, which gives this table

A B  XOR
0 0 | 0
0 1 | 1
1 0 | 1
1 1 | 0

Now you have to pair the 3 and the 15 binary vertically and proceed the XOR operation bit by bit

Bit  A B  XOR
1    1 1 | 0 
2    1 1 | 0
3    1 0 | 1
4    1 0 | 1

I.e. the result of 0b1111 xor 0b0011 is 0b1100, in decimal is 12.