After reading the base64 wiki ...
I'm trying to figure out how's the formula working :
Given a string with length of n
, the base64 length will be
Which is : 4*Math.Ceiling(((double)s.Length/3)))
I already know that base64 length must be %4==0
to allow the decoder know what was the original text length.
The max number of padding for a sequence can be =
or ==
.
wiki :The number of output bytes per input byte is approximately 4 / 3 (33% overhead)
Question:
How does the information above settle with the output length ?
Each Base64 digit represents exactly 6 bits of data. So, three 8-bits bytes of the input string/binary file (3×8 bits = 24 bits) can be represented by four 6-bit Base64 digits (4×6 = 24 bits). This means that the Base64 version of a string or file will be at least 133% the size of its source (a ~33% increase).
Base64 encodes 3 bytes of binary data on 4 characters. So to get the size of the original data, you juste have to multiply the stringLength (minus the header) by 3/4.
Length of data Base64 uses 4 ascii characters to encode 24-bits (3 bytes) of data.
The maximum length in 2732 characters. The result of the function is a varying length character string in CCSID 1208 that contains the bytes of character-string as a Base64-encoded string.
Each character is used to represent 6 bits (log2(64) = 6
).
Therefore 4 chars are used to represent 4 * 6 = 24 bits = 3 bytes
.
So you need 4*(n/3)
chars to represent n
bytes, and this needs to be rounded up to a multiple of 4.
The number of unused padding chars resulting from the rounding up to a multiple of 4 will obviously be 0, 1, 2 or 3.
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