Base64 Encoding of Binary Data

Base64 encoding converts arbitrary binary data into a text string using 64 printable ASCII characters. It exists because many transport protocols (email, JSON, URLs) only reliably handle text, not raw binary bytes.

The Base64 alphabet:

A-Z (0-25), a-z (26-51), 0-9 (52-61), + (62), / (63), with = used for padding.

How Base64 works at the bit level:

1. Take 3 bytes of input (24 bits total)
2. Split into 4 groups of 6 bits each
3. Map each 6-bit value to a character from the Base64 alphabet

Step-by-step example — encoding "Hi":

1. ASCII values: H=72, i=105
2. Binary: 01001000 01101001
3. Add zero-padding to make a multiple of 6 bits: 01001000 01101001 00000000
4. Split into 6-bit groups: 010010 000110 100100 000000
5. Convert to Base64 indices: 18, 6, 36, 0
6. Look up characters: S, G, k, A
7. Since input was 2 bytes (not 3), add one = padding character

Result: "SGk="

Why 6 bits?

The number 64 = 2⁶, so 6 bits can represent values 0-63, mapping perfectly to the 64-character alphabet. Three input bytes (24 bits) divide evenly into four 6-bit groups, which is why Base64 processes data in 3-byte chunks.

The 33% size increase:

Base64 converts every 3 bytes of input into 4 characters of output, a 33% size increase. This is the unavoidable cost of representing binary data as text.

Padding rules:

• 3 input bytes -> 4 Base64 characters (no padding)
• 2 input bytes -> 3 Base64 characters + =
• 1 input byte -> 2 Base64 characters + ==

URL-safe Base64: Replaces + with - and / with _ to avoid conflicts with URL special characters. Used in JWTs, data URIs, and URL parameters.