Bitwise math/Operators/XOR

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XOR is a bitwise comparison operator that returns a true bit if the compared bits in question are different. If they are the same, it returns a false bit.

XOR rules

XOR determines which bits differ in the two binary numbers used as operands.

• 1 xor 1 = 0
• 1 xor 0 = 1
• 0 xor 0 = 0

XOR properties

• Anything xor'd with itself results in 0
• Anything xor'd with 0xF is the same as a "not"
• Anything xor'd with zero results in itself

XOR example

Example: A xor F = 5

Operation	Hexadecimal	Binary	comment
xor	A F	1010 1111	The first and third bits are true. The first, second, third, and fourth bits are true.
=	5	0101	The second and fourth bits are true in ONLY one instance as opposed to two.

• The 8’s and 2's placeholders are the same so they return 0.
• The 4’s and 1’s placeholders are different, therefore return true.

XOR logic table

XOR	0	1	2	3	4	5	6	7	8	9	A	B	C	D	E	F
0	0	1	2	3	4	5	6	7	8	9	A	B	C	D	E	F
1	1	0	3	2	5	4	7	6	9	8	B	A	D	C	F	E
2	2	3	0	1	6	7	4	5	A	B	8	9	E	F	C	D
3	3	2	1	0	7	6	5	4	B	A	9	8	F	E	D	C
4	4	5	6	7	0	1	2	3	C	D	E	F	8	9	A	B
5	5	4	7	6	1	0	3	2	D	C	F	E	9	8	B	A
6	6	7	4	5	2	3	0	1	E	F	C	D	A	B	8	9
7	7	6	5	4	3	2	1	0	F	E	D	C	B	A	9	8
8	8	9	A	B	C	D	E	F	0	1	2	3	4	5	6	7
9	9	8	B	A	D	C	F	E	1	0	3	2	5	4	7	6
A	A	B	8	9	E	F	C	D	2	3	0	1	6	7	4	5
B	B	A	9	8	F	E	D	C	3	2	1	0	7	6	5	4
C	C	D	E	F	8	9	A	B	4	5	6	7	0	1	2	3
D	D	C	F	E	9	8	B	A	5	4	7	6	1	0	3	2
E	E	F	C	D	A	B	8	9	6	7	4	5	2	3	0	1
F	F	E	D	C	B	A	9	8	7	6	5	4	3	2	1	0