**Bitwise NOT (~)**

The bitwise NOT operator is a unary operator, meaning, it works on only one operand. **The NOT operator simply inverts every bit of the operand.**

Sounds familiar?

If you remember from the last article, **Flipping every bit of a binary number produces the One’s Complement of that number**.

Hence, this operator is also called the **Complement Operator**.

**The Truth Table**

**Examples :**

~27

~0011011

= 1100100~8

~1000

= 0111

So, as you could have guessed, the NOT operator is used to produce the Two’s Complement of a number.

Recalling from the previous article.**A Two’s Complement = One’s Complement + 1**

Hence,

Two's Complement of 8 = ~8+1 = -8

Two's Complement of 27 = ~27+1 = -27

**Bitwise AND (&)**

The bitwise AND operator compares each bit of the first operand to the corresponding bit of the second operand. **If both bits are 1, the corresponding result bit is set to 1, else the corresponding bit is set to 0.**

**The Truth Table**

**Examples :**

47 & 84

00101111

& 01010100

-------------

00000100 = 4

27 & 10

00011011

& 00001010

-------------

00001010 = 10

**Bitwise OR (|)**

The bitwise OR operator compares each bit of the first operand to the corresponding bit of the second operand. **If either of the bits is 1, the corresponding result bit is set to 1, else the corresponding bit is set to 0**.

**The OR operator is also called Inclusive OR operator because it includes as true the condition where both the inputs are true. ( 1 | 1 = 1 )**

**The Truth Table**

**Examples :**

27 | 10

00011011

| 00001010

-------------00011011 = 2712 | 10

1100

| 1010

-------------1110 = 14

**Bitwise XOR (^)**

The bitwise XOR operator compares each bit of the first operand with the corresponding bit of the second operand, **and returns 1 only and only if one of the two bits is 1. It returns 0 if both the bits are 0, and also if both the bits are 1.**

For the output to be true, only one of the inputs should exclusively be true. Hence this operator is called as the **Exclusive Or operator.**

**The Truth Table**

Examples :

28 ^ 12

11100

^ 01100

----------10000 = 1612 ^ 16

01100

^ 10000

----------11100 = 2828 ^ 16

11100

^ 10000

----------01100 = 12

Did you notice anything strange in the above examples?

Observe the pattern.

28 ^ 12 = 1612 ^ 16 = 2828 ^ 16 = 12

This is a very interesting property of the XOR operator

A ^ B ^ A = BA ^ B ^ B = A

This specific property forms the base of most of the encryption systems.

Stating it in a very simple terms…

Input ^ Key = Encryption

Encryption ^ Key = Input

XORing Input Data with a Key produces Encrypted dataAnd, XORing the Encrypted data with the Same Key gives back the Input Data.

In the next article we will look at the Bitwise Shift Operators

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