I'm not aware of any serial 1s' complement or 2's complement machines. You've made claims; that doesn't mean that they are true. There is nothing that precludes any representation in an array machine. You are begging the questions by the assumptions that you are making.
-- Shmuel (Seymour J.) Metz http://mason.gmu.edu/~smetz3 ________________________________________ From: IBM Mainframe Assembler List [[email protected]] on behalf of Robin Vowels [[email protected]] Sent: Friday, June 17, 2022 4:54 AM To: [email protected] Subject: Re: When did logical instructions appear? On 2022-06-17 18:04, Seymour J Metz wrote: > FSVO serial. The early electronic machines that I'm aware of were > parallel. > > FWIW, there were papers claiming that 1s' complement was simpler. Not in a serial machine. What's more, I've already pointed out that in an array machine, ones complement was impossible because you only got one look at the operands and the result. The result had to be stored in the same cycle as the operands were available, because the next cycle the sum or difference of the next operands was required to be performed. In a serial machine, the sum of a pair of corresponding bits produces at the same moment the sum bit. > I > believe that the tradeoffs vary depending on the technology used. > > ________________________________________ > From: IBM Mainframe Assembler List [[email protected]] > on behalf of Robin Vowels [[email protected]] > Sent: Friday, June 17, 2022 2:40 AM > To: [email protected] > Subject: Re: When did logical instructions appear? > > ----- Original Message ----- > From: "Paul Gilmartin" > <[email protected]> > To: <[email protected]> > Sent: Friday, June 17, 2022 7:20 AM > > >> On Jun 16, 2022, at 10:43:36, Robin Vowels wrote: >>> >>> Computers have had instructions for signed and unsigned binary >>> since at least 1951. When negative values are expressed using >>> twos complement notation, ordinary addition will give the same >>> result whether the operation is signed or unsigned. >>> >> It puzzles me that some of the oldest computers employed sign- >> magnitude notation when 2's (1's, 10's) complement would have >> needed fewer gates and fewer clock cycles. > > For a serial machine (and most of them were in the early days), > twos complement was the simplest. It needed only one cycle > for add and subtract. Even subtract (complement and add one) > was done in a single cycle, "on the fly". It was unnecessary to > add the one; complement commencing after the first non-zero bit. > > Ones complement was a PITA, because a carry out of the high end > required a 1 to be added in the next cycle. This was no good at > all for array machines such as Pilot ACE, DEUCE, and ACE, > because the word just summed would not have been around > to add the final "1" produced by the carry out -- the arithmetic > unit already working on summing (or subtracting) the next pair > of words. > >> Perhaps an accommodation to the engineers' habits.
