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Two very common connectors used in the eighties were the Centronics parallel port (particularly used for printers) and the RS-232 serial port (particularly used for mice and modems).

Suppose you have a computer with one kind of port and a peripheral with another (particularly, a computer that talks RS-232 and a printer that talks Centronics). Is/was it possible to buy or build a widget to translate between them? (A widget simpler than a full-blown computer, I mean.) It seems to me that the parallel to serial translation would need some kind of shift register. I'm not so sure about the voltage issue. As I understand it, Centronics uses 5V and RS-232 uses 12V. Is there a way to translate between those?

This is only barely Retrocomputing. Almost all the printers I use today (and most people I know) are connected USB or networked. But ports for PCs are still available and as noted below, the companies I dealt with years ago for converters still sell them. But there aren't so many printers these days with serial or parallel ports now that 100M (or even 1G) network ports for printers are dirt cheap, so we'll call it Retro.

There were (still are!) plenty of options:

Add a port to the printer

For example, Okidata Microline printers would typically come standard with a parallel port but you could add a serial port card (I probably still have one around here somewhere). In more recent years I think they even had a network card that used the same interface slot, though I never bothered with that myself.

Add a port to the computer

With PC-compatibles this is trivial, but with other machines not always so easy. Plus there are situations (e.g., 6 terminals plus 2 printers all connected serial to an 8-port statistical multiplexer over a modem connection back to the host) where this is just simply not an option. Plus end-to-end serial has big advantages over parallel - 200 feet without any problem at all.

Converter

These have been available for a long time from Patton (sells nationwide but one of my favorites because they are nearby), B & B and Black Box - all of which still list parallel/serial converters on their web sites.

Voltage is, I think, the least of the conversion issues. The big factor is handshaking. Over the years, I found that parallel handshaking was very reliable but serial...not so much. It seems that some manufacturers just never got serial handshaking to work well, and I sometimes had to resort to large buffers (typically a little box with a Z80 (or similar), 64k of RAM and ports for in & out) to work around the problem. But I think the basic converters typically did their job without a full CPU - just a bunch of glue chips/logic to read a byte in one form and send it out as another.