Ones-complement arithmetic: it lives!

Most hackers know how the twos-complement representation of binary numbers works, and are at least aware that there was an older representation called “ones-complement” in which you negated a binary number by inverting each bit.

This came up on the NTPsec development list recently, with a question about whether we might ever have to port to a non-twos-complement machine. To my utter, gob-smacked astonishment, it turns out ones-complement systems still exist – though, thankfully, not as an issue for us.

I thought I could just mumble something about the CDC 6600 and be done, but if you google “one’s-complement machines” you’ll find that Unisys still ships a series of machines with the brand “Clear-Path Dorado” (latest variant introduced 2015) that are emulations of their old 1100-series mainframes running over Intel Xeon hardware – and these have one’s-complement arithmetic.

This isn’t a practical port blocker for NTPsec, as NTP will never run over the batch OS on these things – it’s about as POSIX-compatible as the Bhagavad-Gita. It’s just weird and interesting that ones-complement machines survive in any form at all.

And a bit personal for me. My father was a programmer at Univac in the 1950s and early ’60s. He was proud of his work. My very first interaction with a computer ever was getting to play a very primitive videogame on the oscilloscope-based video console of a Univac 1108. This was in 1968. I was 11 years old, and my game machine cost $8M and took up the entire ground floor of an office building in Rome, Italy.

Other than the 1100, the ones-complement machines Wikipedia mentions (LINC, PDP-1, and CDC6600) are indeed all long dead. There was a ones-complement “CDC Cyber” series as late as 1989, but again this was never going to implement POSIX.

About other competitors to twos-complement there is less to say. Some of them are still used in floating-point representations, but I can find no evidence that sign-magnitude or excess-k notation have been used for integers since the IBM 7090 in 1959.

There’s a comp.lang.std.c article from 1993 that argues in some technical detail that that a C compiler is not practical on ones-complement hardware because too many C idioms have twos-complement assumptions baked in. The same argument would apply to sign-magnitude and excess-k.