This is pretty cool. There were some LFSR-PC CPUs back in the 70s such as the TMS 1000 used in the Speak&Spell https://github.com/mikeakohn/tms1000_fpga (its Data Manual omits mention of this, but the Programmer's Reference Manual does mention it https://ia800306.us.archive.org/27/items/bitsavers_tiTMS1000...), and of course the Atari 2600 TIA raster generator is famous for using an LFSR counter for horizontal position. Ken Shirriff has also documented the use of an LFSR counter for tone generation in the UM66T greeting-card music chip http://www.righto.com/2021/12/reverse-engineering-tiny-1980s... and for Pentium self-test circuitry http://www.righto.com/2025/01/pentium-carry-lookahead-revers... and for DTMF tone generation.

It occurred to me recently that an LFSR-pc CPU could avoid having an address field in its conditional jump instructions, instead doing something like complementing a PC bit. There have been conventional counter-based CPUs that did something like this: Data General's NOVA and HP's RPN calculators had conditional-skip instructions which would skip over the next instruction without executing it if the condition was false. But it was usually a jump instruction, so it didn't really save you space. (The TMS 1000's conditionals also worked this way, but could only skip branch and call instructions.)

By contrast, in an LFSR, complementing a bit or incrementing the value takes you potentially far away in the address sequence. The assembler might have to insert NOPs to resolve the occasional collision.

The TMS 1000 program counter had an additional twist: it was only 6 bits, but to enable programs of more than 64 instructions, there were multiple 64-byte "pages" of ROM. The page address register was potentially updated on branches, calls, and returns, but not for normal program sequencing. I'm not sure if this actually saved any transistors, but it meant that normal branch instructions only needed a 6-bit field. An additional "load page buffer" instruction was needed for far jumps and calls, and the page buffer register remained loaded with the return page until the return instruction. (Subroutine calls within subroutines were not supported.)

https://electronics.stackexchange.com/questions/186762/first... claims that the TMS 1000 had 8000 transistors, which seems really inefficient compared to things like the 4004 and the MuP21.

I had a lot of fun writing this and it is great to see this submitted here, I just did it to see what was possible. It is an incredibly niche processor with little practical use. If you have any questions let me know.

I have also started contracting in the UK and I'm looking for work, details are in my profile.

I have used the same LFSR-PC trick for my relay CPU:

https://github.com/artemonster/relay-cpu

Instead of having 24 relays to have a 12bit incrementer (a full adder requires 4 DPDT relays per bit or 2 quad relays) I only have 3 relays for 3 XORs :)

I got lost in the weeds following links for a bit. Had not heard of LFSR before, which I think is odd, and then onto some other things like Subleq and OISC. I've at least seen other OISCs before, it might have even come up on hn around x86 mov, I'm not sure. I really regret not taking more hardware/electronics courses in college.

Wouldn't this make it somewhat more challenging for assemblers/compilers to emit branch instructions with target PC offsets?

For instance, the offset of an instruction two instructions away would be calculated as `lfsr(lfsr(pc))` (off-by-one bugs notwithstanding), right?

LFSR IP seems like one of the optimizations that would show up in a CPU designed for the absolute lowest energy per operation. Sadly many of the most interesting low energy optimizations will be at the analog/transistor level-- or even from optimizing across that boundary--, taking them out of the realm of hobbiests.

instruction set design is reminiscent of PDP8