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Comment by ebingdom | Hacker News Reader

> Let’s begin by the base64 notation. The cardinality of each byte is 64 so it takes 3 bytes in base64 to represent 2 bytes of actual value.

Wait, what? I thought it takes 4 base-64 digits to represent 3 bytes of data. Not 3 base-64 digits to represent 2 bytes of data.

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base64 means the "vocabulary" used has 6 bits (2^6 = 64). Hence, to complete a full number of bytes (without using any padding), you need 4 b64-letters:

    4 * 6 = 24 = 8 * 3

So, you're correct... the exact amount of bytes that it takes to represent "actual" bytes goes like this:

    Actual bytes | b64 bytes required | overhead
    1            | 2                  | 2x
    2            | 3                  | 1.5x
    3            | 4                  | 1.33x
    4            | 6                  | 1.5x
    5            | 7                  | 1.4x
    6            | 8                  | 1.33x
    7            | 10                 | 1.43x
    8            | 11                 | 1.37x
    9            | 12                 | 1.33x

EDIT: As you can see, this averages with an overhead of between 33% (best case scenario where the encoding requires no padding, happens every 3 rows above) and something like 37%, decreasing with the number of bytes being encoded and approaching the minimum, 33% (e.g. to encode 1024 bytes, you need 1366 b64 digits, an overhead of 1.333984375x).

Maybe they're using a 9-bit byte? :)

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