3-bit encoding = Octal; 4-bit encoding = Hexadecimal; 5-bit encoding =?

Question

Is there an encoding that uses 5 bits as one group to encode a binary data?

A-Z contain 26 chars and 0-9 contain 10 chars. There are totally 36 chars which are sufficient for a 5-bit encoding (32 combinations only).

Why don't we use a 5-bit encoding instead of Octal or Hexadecimal?

Answer 1

Yes. It's Base32. Maybe the name would be Triacontakaidecimal but it's too long and hard to remember so people simply call it base 32. Similarly there's also Base64 for groups of 6 bits

Base32 is much less common in use than hexadecimal and base64 because it wastes to much space compared to base64, and uses an odd number of bits compared to hexadecimal (which is exactly divisible by 8, 16, 32 or 64). 6 is also an even number, hence will be better than 5 on a binary computer

Answer 2

Sure, why not:

Welcome to Clozure Common Lisp Version 1.7-dev-r14614M-trunk  (DarwinX8664)!
? (let ((*print-base* 32)) (print 1234567))
15LK7 
1234567
? (let ((*print-base* 32)) (print (expt 45 19)))
KAD5A5KM53ADJVMPNTHPL 
25765451768359987049102783203125
? 

Answer 3

As mentioned in a comment by @S.Lott, base64 (6-bit) is often used for encoding binary data as text when compactness is important.

For debugging purposes (e.g. hex dumps), we use hex because the size of a byte is evenly divisible by 4 bits, so each byte has one unique 2-digit hex representation no matter what other bytes are around it. That makes it easy to "see" the individual bytes when looking at a hex dump, and it's relatively easy to mentally convert between 8-bit binary and 2-digit hex as well. (In base64 there's no 1:1 correspondence between bytes and encoded characters; the same byte can produce different characters depending on its position and the values of other adjacent bytes.)