iOS Base 64 encoding

[Nnavick]

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I want to write an algoritm that does bade64 encoding.

I saw in Wikipedia a chart but I don't understand the last part :
Text context M ASCII is 77 the binary part I understood but I dont understand the index part ,how they got 19??


Text content M a n
ASCII 77 97 110
Bit pattern 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 0
Index 19 22 5 46
Base64-encoded T W F u


http://en.m.wikipedia.org/wiki/Base64
Thanks!!!

 

[sammich]

The 6-bit values are converted into their base10 equivalents.

16 + 2 + 1 = 19

http://www.wikihow.com/Convert-from-Binary-to-Decimal

 

[KnightWRX]

Base 64 encoding is basically taking 8 bit characters and making them 6 bit.

Considering binary positions indicate a certain power of 2 value, you can simply add up the values of the 1s (128 64 32 16 8 4 2 1) and lookup the ASCII value to get the indices :

0 1 0 0 1 1 0 1 - (64 + 8 + 4 + 1) - 77 - M
0 1 1 0 0 0 0 1 - (64 + 32 + 1) - 97 - a
0 1 1 0 1 1 1 0 - ( 64 + 32 + 8 + 4 + 2) - 110 - n

Now, since we're taking these and converting them to 6 bit (with 2 leading 00s), we need to split this up evenly to not lose any information (we can't just bit shift by 2, we'll lose the 2 1 and positions). So we take the whole 24 bit chain, (3 x 8 bit characters) and split them up into 4 6 bit chains.

0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 0

Add 2 leading 0s to each and you now get how base64 encoded string to which you can apply our same math as earlier :

0 0 0 1 0 0 1 1 - (16 + 2 + 1) - 19
0 0 0 1 0 1 1 0 - (16 + 4 + 2) - 22
0 0 0 0 0 1 0 1 - (4 + 1) - 5
0 0 1 0 1 1 1 0 - (32 + 8 + 4 + 2) - 46

This is the tricky part. These aren't ASCII characters. You can't simply store this number in a char and then printf("%c"); the output and hope to get a valid Base64 string. These are "index" values to the Base64 Alphabet. It is defined in RFC 3548 :

                Table 1: The Base 64 Alphabet

      Value Encoding  Value Encoding  Value Encoding  Value Encoding
          0 A            17 R            34 i            51 z
          1 B            18 S            35 j            52 0
          2 C            19 T            36 k            53 1
          3 D            20 U            37 l            54 2
          4 E            21 V            38 m            55 3
          5 F            22 W            39 n            56 4
          6 G            23 X            40 o            57 5
          7 H            24 Y            41 p            58 6
          8 I            25 Z            42 q            59 7
          9 J            26 a            43 r            60 8
         10 K            27 b            44 s            61 9
         11 L            28 c            45 t            62 +
         12 M            29 d            46 u            63 /
         13 N            30 e            47 v
         14 O            31 f            48 w         (pad) =
         15 P            32 g            49 x
         16 Q            33 h            50 y

That's where TFWu (19 22 5 46) comes from.