Definition of Base64

Base64 is a encoding scheme used to represent arbitrary data with US-ASCII-compatible strings. The alphabet of an encoded string consists of 2^6 + 1 = 65 characters, where the first 64 characters represent the actual values and the last one (=) is used for padding when needed. Each of the 2^6 = 64 value characters represents 6 bits of the data.

See below for a listing of the full alphabet:

Encoding 24 bits (3 bytes) of data, takes 4 characters in Base64 (4 * 6 bits = 24 bits). If the data is not a multiple of 3 bytes, we have to append zero-bytes (i.e. 00000000) until it is (at most we have to append 2 such bytes). Afterwards, we split the data into 3-byte chunks, to get a sequence of so-called quanta and proceed by encoding each quantum as follows.

Encoding some data with up to 3 bytes looks like this:

The number of characters at the end of the Base64 string to replace with the padding character (=) can be calculated as follows for a data with n bytes:

The number of required value bits v and padding bits p are easy to calculate for a given number of data bits n:

Note, that 24 is the smallest common multiple of 6 and 8.

Observations

• Base64 strings are invalid (i.e., cannot be decoded) if they contain any characters outside the alphabet given above.
• Due to the padding, the length (number of characters) in valid Base64 strings is always divisible by 4. Therefore, Base64 strings are also invalid, if this is not the case.
• Base64 is of course fully reversible: decode64(encode64(d)) = d for some arbitrary data d with n >= 0 bytes. Therefore, libraries usually provide an encode and a decode function.