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Base64 Algorithm

Deep dive into the mathematics and bitwise mechanics behind the Base64 encoding standard.

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The core concept of the Base64 algorithm is grouping input data at the bit level. While standard bytes are 8 bits wide (values 0–255), Base64 uses 6-bit units (26 = 64 distinct values, 0–63).

The 24-Bit Common Multiple

The least common multiple of 8 (a byte) and 6 (a Base64 unit) is 24 bits:

  • Input: 3 bytes × 8 bits = 24 bits
  • Output: 4 characters × 6 bits = 24 bits

Whenever you have 3 bytes of raw binary data, Base64 maps them cleanly into exactly 4 printable ASCII characters without leftover bits.

Visual Bit-Splitting Example: "Man"

Let's walk through how the 3-letter ASCII word Man is converted:

Step Byte 1 ('M') Byte 2 ('a') Byte 3 ('n')
ASCII Char M a n
ASCII Dec 77 97 110
8-Bit Binary 01001101 01100001 01101110
24-Bit Stream 010011010110000101101110
6-Bit Groups 010011 010110 000101 101110
Decimal Index 19 22 5 46
Base64 Char T W F u

Thus, the string Man encodes to TWFu.