Besides binary, decimal, hex, oct, are there encryption algorithms based on exotic/other numbering systems? We all know there is Base 10, Base 16, etc. Are there encryption algorithms out there based on different or unique Base-N numbering systems?
There's FF1 and FF3, which are Format Preserving Encryption methods that can use an arbitrary base internally.  This can be useful, for example, if you are encrypting a fixed length alphanumeric field, it would make sense to use base 36 (radix=36) or base 62 (if upper and lower cases are distinguished).