Jeff Epler's blog2026-03-09T20:55:10ZPhotos, electronics, cnc, and moreJeff Eplerjepler@unpythonic.netradix40 encoding2026-03-09T20:55:10Z2026-03-09T20:55:10Zhttps://gamma.unpythonic.net/01773089710
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<p><br>I was inspired to design an original(?) text encoding for tiny embedded
computers. It is, however, similar to <a href="https://en.wikipedia.org/wiki/DEC_RADIX_50">DEC RADIX 50</a> from 1965. (That's 50₈=40₁₀).
Since 40³<65536, it is possible to store 3 symbols in each 16 bit word.
<p>In radix 40 you get the 26 basic alphabetic characters, 10 digits, and 4
additional symbols. I chose:
<ul>
<li>End of string
<li>Space (ASCII 32)
<li>Exclamation point (ASCII 33)
<li>Double quote (ASCII 34)
</ul>
<p>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.
<p>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
<tt>x<-x*8; tmp<-x; x<-x*4; x<=x+tmp</tt>) since the MC6800 has no multiply
instruction.
<p>Here are the not quite matching Python encoder
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<p>And decoder/test program in m6800 assembly:
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<p>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.
<p>The m6800 decoder can over-read the data by 1 byte, which seldom poses a problem in such environments.