Here's a document that I typed to myself and last updated who knows how long ago:

Base64 Encoding Algorithm

Base64 algorithm is designed to encode any binary data, a stream of bytes, into a stream of 64-printable characters.

Base64 encoding algorithm was first presented in "RFC 1421 - Privacy Enhancement for Internet Electronic Mail: Part I: Message Encryption and Authentication Procedures" in 1993 by John Linn. It was later modified slightly in "RFC 1521 - MIME (Multipurpose Internet Mail Extensions) Part One: Mechanisms for Specifying and Describing the Format of Internet Message Bodies" in September 1993 by N. Borenstein, et al..

The 64 printable characters used by Base64:
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
15 P 32 g 49 x
16 Q 33 h 50 y
The encoding process is to:

  • Divide the input bytes stream into blocks of 3 bytes.
  • Divide the 24 bits of a 3-byte block into 4 groups of 6 bits.
  • Map each group of 6 bits to 1 printable character, based on the 6-bit value.
  • If the last 3-byte block has only 1 byte of input data, pad 2 bytes of zero (\x0000). After encoding it as a normal block, override the last 2 characters with 2 equal signs (==), so the decoding process knows 2 bytes of zero were padded.
  • If the last 3-byte block has only 2 bytes of input data, pad 1 byte of zero (\x00). After encoding it as a normal block, override the last 1 character with 1 equal signs (=), so the decoding process knows 1 byte of zero was padded.
  • Carriage return (\r) and new line (\n) are inserted into the output character stream. They will be ignored by the decoding process.


Example 1: Input data, 1 byte, "A". Encoded output, 4 characters, "QQ=="
Input Data A
Input Bits 01000001
Padding 01000001 00000000 00000000
\ \ \
Bit Groups 010000 010000 000000 000000
Mapping Q Q A A
Overriding Q Q = =

Example 2: Input data, 2 bytes, "AB". Encoded output, 4 characters, "QUI="
Input Data A B
Input Bits 01000001 01000010
Padding 01000001 01000010 00000000
 \ \ \
Bit Groups 010000 010100 001000 000000
Mapping Q U I A
Overriding Q U I =

Example 3: Input data, 3 bytes, "ABC". Encoded output, 4 characters, "QUJD"
Input Data A B C
Input Bits 01000001 01000010 01000011
\ \ \
Bit Groups 010000 010100 001001 000011
Mapping Q U J D