===== Base-64 Encoding =====

**Multipurpose Internet Mail Extensions (MIME)** is the official format for internet emails. Emails are transmitted to recipients via the **SMTP** (Simple Mail Transfer Protocol), which only supports the transfer of **7-bit ASCII characters**. To handle binary data in email attachments, the MIME standard provides several encoding methods, one of the most common being **Base-64 encoding**.

Below is an example of an email with an attachment, showing the source data that email programs interpret:

<code>
Content-type: multipart/mixed; boundary="frontier"
MIME-version: 1.0
--frontier
Content-type: text/plain
This is the body of the message.
--frontier
Content-type: application/octet-stream
Content-transfer-encoding: base64
gajwO4+n2Fy4FV3V7zD9awd7uG8/TITP/vIocxXnnf/5mjgQjcipBUL1b3uyLwAVtBLOP4nV
AhSzlZnyLAF8na0n7g6OSeej7EjlF/aglS6ghfju FgRr+OX==
--frontier--
</code>

The second and third lines from the end show **Base-64 encoded data**.

=== What is Base-64 Encoding? ===

**Base-64 encoding** (or more generally, data representation) is based on a set of 64 symbols. It's essentially like converting data into a 64-base numbering system. The encoding works by grouping the data into **6-bit chunks**.

The Base-64 encoding scheme uses the following symbol set:

  * **0..25** → 'A'..'Z'
  * **26..51** → 'a'..'z'
  * **52..61** → '0'..'9'
  * **62** → '+'
  * **63** → '/'

This gives us 64 unique symbols to represent binary data. The encoding is done so that every **3 bytes** of input data is converted into **4 characters** of Base-64 output.

=== Example of Base-64 Encoding ===

Let's take a simple binary string and encode it in Base-64:

Input:
''001100110011''

We split it into two 6-bit groups:

''001100 , 110011''

These groups correspond to decimal values **12** and **51**. Using the Base-64 table:
  * 12 → 'M'
  * 51 → 'z'

Thus, the Base-64 encoding of `001100110011` is **Mz**.

=== Padding and Handling Non-Multiples of 3 Bytes ===

Base-64 encoding operates on blocks of 3 bytes (24 bits). If the input data isn’t divisible by 3, padding is added to complete the block. This padding is represented by the **'='** symbol. Here are two examples:

===Example 1 ===
 
Encoding the byte `00000001`

1. We first extend it to 3 bytes by adding two zero bytes: ''00000001 00000000 00000000''.

2. Split this into 6-bit groups: ''000000 010000 000000 000000''.

3. The result is ''AQ==''.

===  Example 2: === 

Encoding the bytes ''00000010 00000001''

1. Extend to 3 bytes: ''00000010 00000001 00000000''.

2. Split into 6-bit groups: ''000000 100000 000100 000000''.

3. The result is ''AgE=''.

=== Base-64 Decoding === 

Decoding Base-64 involves reversing the process, converting each Base-64 character back into its 6-bit binary equivalent. The binary groups are then combined to form the original data. The number of **'='** symbols at the end of the encoded data tells us whether the last byte is incomplete, helping determine whether to interpret the last 6 or 12 bits of the encoded string.

=== Special Considerations=== 

  * Base-64 encoded data can contain **line break characters** to help manage long strings. These line breaks (or any other non-Base-64 characters) should be ignored during decoding.
  * One major advantage of Base-64 encoding is that it safely encodes binary data into a **text-friendly format**, making it ideal for transmission over protocols that only support text (like email and HTTP headers).

=== Real-World Application of Base-64 ===

In everyday internet use, Base-64 encoding is used in various places, such as:

  * Email attachments (as shown in the MIME example).

  * Embedding image data in HTML or CSS files.

  * Encoding sensitive data in URL query parameters to ensure safe transmission.

For instance, in the email example above, the binary content of the attachment is encoded into Base-64 so it can be transmitted through the SMTP protocol, which only supports 7-bit ASCII characters.