How does Base32 (or any Base2^n) work exactly?

How does Base32 (or any Base2^n) work exactly?
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Base36: 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ

Good encoding for binary data in textual contexts. Such as where you have parameter inputs or database fields that are constrained and only accept certain characters. The lack of spaces means that it can be used on the command-line easily. Example use: IRC channel names.

Base64: 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz

Same as above but it adds lower-case alphabet characters. This is important because as you restrict the number of characters allowed in a byte: the length of the string goes up massively. With more characters the coding is more efficient. Example use: YouTube video ids.

Base92: "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz~!@#$%^&*()_+{}\"?`-=[];',./|"

Base92 is every character you can make on a standard key-board (I've replaced space with pipe here.) It includes many characters that have special meanings on the command-line or may be used as delimiters in text-based protocols. So while this offers a more 'efficient' encoding scheme for binary data it may break in some contexts. It's best where the input allows for typical formatting. Example use: forum / chat messages.

BaseN encoding schemes are interesting because they allow you to use standard text-fields in many systems to store binary data. The most well-known here is base64 which allows browsers to embed whole files as text and store them directly in the HTML. Some sites use these for optimization hacks.

Not implementing the RFC, is not implementing Base32, changing the order, or using 32 emoji does not make it Base32. Put another way, you can change the order of characters in Base64, or use a different dictionary, and indeed there are several variants of that too (BinHex4, Uuencoding, Base64Url, B64) - there are specific implementation detail concerns there too.

Base64 won out as a reasonably dense way to encode binary data in 7-bit safe ASCII for use in email, and later http headers (where spacing and line length may be modified in transit, and some ASCII characters are prohibited - eg 0x00/null). Part of the reason is; bit-grouping makes encode/decode simpler (you can use bit shifting). Something like ASCII85/Base85 which is a more dense encoding, and close to the maximum you can get in 7 bit safe ASCII (94 characters 33-126 if space is important, 95 if space quantity can be preserved) but you have to use multiply/divide instructions. The union of bit-shift speed (power of 2) and 7-bit safe ASCII characters (max 94 values) is: binary, base4, octal, hexadecimal, base32, and base64.

For human readability, especially verbal communication, hexadecimal or base32 are advantageous in that they are more dense than decimal, can be generated via bit-shifting vs more complex processor instructions, but you needn't also communicate the character's case (unlike Base64).

Better IMO is base 32 with U (obscenity), 0/O (ambiguity), and I (ambiguity) removed.