Python Bitwise XOR Operator
Binary language is the language of a computer. All the inner mechanisms of a computer happen concerning bits. Bitwise operators are the set of operators that allow the programmer to perform bitwise operations on integers. These operators allow the programmer to manipulate the lower-level data in a computer. There are a total of six bitwise operators in Python:
- Bitwise AND
- Bitwise OR
- Bitwise NOT
- Bitwise XOR
- Bitwise right shift
- Bitwise left shift
This article discusses the Bitwise XOR operator with examples.
- When we apply a bitwise operator on two operands, the integer values are converted into their binary forms-into bits.
- Then, the operator performs the operation bit-by-bit on every individual bit.
- After the operation, the binary number is converted to decimal form and returned as the output.
Now, let us understand the operation of Bitwise XOR:
- It is called "Exclusive OR". It excludes the 1 | 1 -> 1 condition from 'or'.
- It is a binary operator - performed between two operands.
- Representation: a ^ b where 'a' and 'b' are two operands.
- Return value: It returns an integer when performed between two integers and a Boolean value when performed between two Boolean values.
- The given two integers are converted into binary form.
- In the two binary notations:
After xor is performed on all the bits, the resultant binary number is converted back to decimal and returned.
- If both corresponding bits are the same - (1 ^ 1), (0 ^ 0), it returns 0.
- If both corresponding bits are different - (1 ^ 0), (0 ^ 1), it returns 1.
The truth table of XOR:
|Bit 1 (operand 1)
||Bit 2 (operand 2)
Let us understand the concept using an example:
If we want to perform:
3 ^ 4:
1. Both the integers are converted into binary forms:
3 -> 0 1 1
4 -> 1 0 0
2. Now, xor is applied bitwise:
3. Finally, the resultant binary number is converted back to its decimal form.
1 1 1 represents 7
4. Output -> 7
3 ^ 4 -> 7
Now, for the same operands, let us write a code for xor:
On Boolean values:
We can perform xor on Boolean values. When we operate on two integers, 1 is equivalent to Boolean True, and 0 is equivalent to Boolean False.
||Operand 1 ^ Operand 2
Structure of outputs:
- If we performed xor on a and b -> a ^ b. As a result, we got some integer c (a ^ b -> c) then,
- If we perform xor on c and a, b will be the output -> c ^ a -> b
- If we perform xor on c and b, a will be the output -> c ^ b -> a
Let us take the above example:
If a ^ b -> c
c ^ a -> b
c ^ b -> a
- If we know the output and one operand, we can find the other operand using this relation.
- This relation is only possible with xor because of its truth table.
Role of xor in cryptography:
The above relation got xor a small role in cryptography models.
- If a person 'A' wants to send a numerically encoded message to another person 'B' confidentially, he needs one more simple cover for the encoded message.
- Both A and B will have a secret key known to each other beforehand.
- Now, A will XOR the message with the secret key and send it to B.
- After receiving, B can perform xor again with the received xor result and secret key and get the message.
If A wants to send the message 3 to B and their secret key is 4
3 ^ 4 -> 5.
A will send 5 to B.
B already knows the secret key is 4.
He will decrypt the message using xor again:
5 ^ 4 -> 3
Message successfully received.
- This method is the simplest, and so is the weakest cryptography method.