Jeff Epler's blog

radix40 encoding

I was inspired to design an original(?) text encoding for tiny embedded computers. It is, however, similar to DEC RADIX 50 from 1965. (That's 50₈=40₁₀). Since 40³<65536, it is possible to store 3 symbols in each 16 bit word.

In radix 40 you get the 26 basic alphabetic characters, 10 digits, and 4 additional symbols. I chose:

• End of string
• Space (ASCII 32)
• Exclamation point (ASCII 33)
• Double quote (ASCII 34)

The choice of 3 characters that are adjacent in ASCII saved code size on the decoder; initially I thought maybe "-" and "." would be useful choices.

Unlike RADIX 50, the encoding is arranged so that no division or remainder operation is needed. Instead, at each step of decoding, a 24 bit temporary value is multiplied by 40 and the top byte gives the output code. In the assembler vesion, the multiplication is coded as x<-x*8; tmp<-x; x<-x*4; x<=x+tmp) since the MC6800 has no multiply instruction.

Here are the not quite matching Python encoder

(Embedded not available - View epvenhla/b40.py on codeberg.org or download raw)

(Embedded not available - View epvenhla/b40.asm on codeberg.org or download raw)

The implementation costs 90 bytes of code and 6 bytes of zero-page (which can be used for other purposes when the routine is not running). I estimate you'd need somewhat above 320 characters of text in your program for it to be a benefit.

The m6800 decoder can over-read the data by 1 byte, which seldom poses a problem in such environments.

By the way, this post debuts improved code embeds from forgejo. On my end, I just have to write [junk epvenhla/b40.py [lang python]] and the blog renderer does the rest!

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