turner@sdti.UUCP (Prescott K. Turner) (09/09/88)
In article <1285@mcgill-vision.UUCP> mouse@mcgill-vision.UUCP (der Mouse) writes: >By the way, does anyone know of a non-mechanical digital calculator or >computer that isn't essentially binary? A couple of years ago I attended a presentation by Prof. William Kahan of U.C. Berkeley. He had an HP calculator with him which as I recall adhered to the IEEE 854 standard for floating point using _decimal_. An example of decimal integers would be better in some ways, but given the stringent rounding requirements of the IEEE floating point standards, this calculator's essence could only be called decimal. -- Prescott K. Turner, Jr. Software Development Technologies, Inc. 375 Dutton Rd., Sudbury, MA 01776 USA (508) 443-5779 UUCP:genrad!mrst!sdti!turner
stevev@uoregon.uoregon.edu (Steve VanDevender) (09/10/88)
In article <297@sdti.UUCP> turner@sdti.UUCP (Prescott K. Turner, Jr.) writes: >In article <1285@mcgill-vision.UUCP> mouse@mcgill-vision.UUCP (der Mouse) >writes: >>By the way, does anyone know of a non-mechanical digital calculator or >>computer that isn't essentially binary? > >A couple of years ago I attended a presentation by Prof. William Kahan >of U.C. Berkeley. He had an HP calculator with him which as I recall >adhered to the IEEE 854 standard for floating point using _decimal_. >An example of decimal integers would be better in some ways, but given >the stringent rounding requirements of the IEEE floating point standards, >this calculator's essence could only be called decimal. > All HP calculators that I've ever seen use BCD floating point (ones that I've used are the 11C and 41C, but I've played with the 15C, 34C and 28C). Most older HP calculators use a 7-byte BCD floating point format with a 10 digit mantissa and 2 digit exponent, with single digits holding the mantissa and exponent signs, and what is essentially a bias 1000 exponent (999 represents an exponent of -1, 901 is -99, and 001-099 are positive exponents). The 28C and 28S (and presumably the 18C and 17S and so on) use a 12 byte mantissa and 3 byte exponent which can range from -499 to +499. HOWEVER, the CPUs of all these machines are essentially binary, in that they can handle non-BCD quantities and store data in bits--not in trinary or whatever. -- Steve VanDevender uoregon!drizzle!stevev stevev@oregon1.BITNET "Bipedalism--an unrecognized disease affecting over 99% of the population. Symptoms include lack of traffic sense, slow rate of travel, and the classic, easily recognized behavior known as walking."
lvc@cbnews.ATT.COM (Lawrence V. Cipriani) (09/10/88)
>In article <1285@mcgill-vision.UUCP> mouse@mcgill-vision.UUCP (der Mouse) >writes: >By the way, does anyone know of a non-mechanical digital calculator or >computer that isn't essentially binary? I heard of a base -2 computer, that was built. For those that don't know how this would work here is a short table of numbers in base -2. 4 -2 1 ----------------- 0 + 0 + 0 = 0 0 + 0 + 1 = 1 0 + 1 + 0 = -2 0 + 1 + 1 = -1 1 + 0 + 0 = 4 1 + 0 + 1 = 5 1 + 1 + 0 = 2 1 + 1 + 1 = 3 It's been so long, I forget where I read about it. As I recall the authors conclusion was that this technique wasn't worth the trouble. -- Larry Cipriani, AT&T Network Systems, Columbus OH, cbnews!lvc lvc@cbnews.ATT.COM
roy@phri.UUCP (Roy Smith) (09/11/88)
mouse@mcgill-vision.UUCP (der Mouse) writes: > By the way, does anyone know of a non-mechanical digital calculator or > computer that isn't essentially binary? There are of course, lots of BCD and similar machines around. Mostly older ones, but even a few new machines (mostly hand-held calculators and the like). But, BCD is really binary underneath in that the actual logic signals are binary, so I don't think that really answers der Mouse's question. I vaugely remember reading about a new RAM technology in which each memory cell stored one of 4 different voltage levels. This was converted on-chip to two convention binary bits. Unfortunately, I can't remember anything about it other than a nagging suspicion that I probably read about it in either IEEE Transactions on Computers or IEEE Spectrum somewhere in the past year. On the other hand, my brain could be playing tricks on me. The bottom line is that digital and binary are essentially synonymous, although I suppose in theory you could define digital as discrete and have trinary, etc. logic. No, Tri-State (probably a tm of somebody) doesn't count. -- Roy Smith, System Administrator Public Health Research Institute {allegra,philabs,cmcl2,rutgers}!phri!roy -or- phri!roy@uunet.uu.net "The connector is the network"
lmiller@venera.isi.edu (Larry Miller) (09/11/88)
In article <297@sdti.UUCP> turner@sdti.UUCP (Prescott K. Turner, Jr.) writes: >In article <1285@mcgill-vision.UUCP> mouse@mcgill-vision.UUCP (der Mouse) >writes: >>By the way, does anyone know of a non-mechanical digital calculator or >>computer that isn't essentially binary? > There was also the IBM 1620, a BCD machine. Yes, decimal, but all arithmetic was performed using table lookup, floating point in software, so I guess it could be called a nonbinary machine. Larry Miller lmiller@venera.isi.edu (no uucp) USC/ISI 213-822-1511 4676 Admiralty Way Marina del Rey, CA. 90292
u-dmfloy%sunset.utah.edu@utah-cs.UUCP (Daniel M Floyd) (09/11/88)
I've been toying with an idea along these lines for a while.
I've done some preliminary research and it's real sketchy.
The theme is along the trinary and up system. I don't think
digital systems like this have ever been built. Obviously
we can't count the n-ary as n goes to infinity because that's an
analog computer. A major problem with anything except binary (I'm
refering to BCD etc here too), is achieving the third, fourth, and
nth stable state. I can't count tri-state (i.e. bus circuits). The
third state with them is floating. If the bus wants high, the
float says "ok". Same if the bus wants low. For true trinary, the
circuit would complain if the bus tried any other level than what
it wanted. (I hope everyone doesn't mind the anthropomorphism.)
I've looked at several alternative trinary logic levels. No one
has given me a convincing argument about which is correct yet.
For example:
Trinary 'AND':
0 1 2 0 1 2
========= =========
0 | 0 0 0 0 | 0 0 0
1 | 0 1 2 1 | 0 1 2
2 | 0 2 2 2 | 0 2 1
Both have merits. I supose you could define them as AND2 and AND1.
Let's see what all of you have to say.rob@kaa.eng.ohio-state.edu (Rob Carriere) (09/11/88)
mouse@mcgill-vision.UUCP (der Mouse) writes: > By the way, does anyone know of a non-mechanical digital calculator or > computer that isn't essentially binary? Some people working on optical digital circuitry are considering using trinary, as that seems to fit well with the physics of some of the materials. So who knows, maybe 50 years from now Der Katze will post the question ``is there any computer that is not essentially trinary?'' :-) Rob Carriere
joe@modcomp.UUCP (09/12/88)
u-dmfloy@sunset.utah.edu.UUCP writes [edited]: > I've been toying with an idea [on trinary and up logic]. I've done some > preliminary research and it's real sketchy. I've looked at several > alternative trinary logic levels. No one has given me a convincing > argument about which is correct yet. > > For example; Trinary 'AND': > > 0 1 2 0 1 2 > ========= ========= > 0 | 0 0 0 0 | 0 0 0 > 1 | 0 1 2 1 | 0 1 2 > 2 | 0 2 2 2 | 0 2 1 > > > Both have merits. I suppose you could define them as AND2 and AND1. > > Let's see what all of you have to say. I haven't been able to divine what your underlying theories are from just the logic charts you presented, so I remain unconvinced that either is valid. My own pet theory is that n-ary logic should be based on analog logic. By that reasoning, AND returns the lowest of the m input values and OR returns the highest. Inversion should simply flip across the n-ary range. For example, let's look at trinary: AND 0 1 2 OR 0 1 2 INVERSION ========= ========= ===== 0 | 0 0 0 0 | 0 1 2 0 | 2 1 | 0 1 1 1 | 1 1 2 1 | 1 2 | 0 1 2 2 | 2 2 2 2 | 0 It should be possible to build XOR gates, adders, and so on with this logic. However, I haven't tried it. Any takers? More to the point, what have you computer scientists out in net-land, who surely have studied this subject to death decades ago, have to say? -- Joe Korty "flames, flames, go away uunet!modcomp!joe come back again, some other day"
henry@utzoo.uucp (Henry Spencer) (09/12/88)
In article <3473@phri.UUCP> roy@phri.UUCP (Roy Smith) writes: > I vaugely remember reading about a new RAM technology in which each >memory cell stored one of 4 different voltage levels. This was converted >on-chip to two convention binary bits. Unfortunately, I can't remember >anything about it... 4-state *ROMs*, not *RAMs*, are already in use to a modest extent. It's one more way of getting somewhat higher memory density, and apparently it does work all right. Nothing but the on-chip circuitry ever sees it. -- NASA is into artificial | Henry Spencer at U of Toronto Zoology stupidity. - Jerry Pournelle | uunet!attcan!utzoo!henry henry@zoo.toronto.edu
albaugh@dms.UUCP (Mike Albaugh) (09/13/88)
From article <6266@venera.isi.edu>, by lmiller@venera.isi.edu (Larry Miller): > There was also the IBM 1620, a BCD machine. Yes, decimal, but > all arithmetic was performed using table lookup, floating point > in software, so I guess it could be called a nonbinary machine. There were _lots_ of BCD (and bi-quinary) machines back when 16K was a lot of memory and a large percentage of problems needed mainly I/O with a few calculations on each item. The size and speed of the decimal to binary and back conversion routines would have made them the major bottleneck. Incidentally, one of the neatest things about the 1620 was that numbers of arbitrary size could be added/subtracted/multiplied/divided (as long as they fit in memory). I know at least one number-theory freak who resented the "restriction" of only 256 byte long numbers when we upgraded to a System/360. Anyway, the 1620 was still "binary", in the sense of any one signal being in one of two states. The Soviets built a balanced base 3 (radix -3) machine in the late fifties (reported in IEEE transactions, as I recall), but it too used binary logic, with each digit stored as two bits. I believe Signetics built a fast math chip of some sort (Maybe a Multiplier?) which actually used base four inside (four discrete current levels in IIL) and converted to binary TTL outside. This was written up in EDN or the like about 1980. > Larry Miller lmiller@venera.isi.edu (no uucp) | Mike Albaugh ({decwrl!turtlevax!}weitek!dms!albaugh) voice: (408)434-1709 | Atari Games Corp (Arcade Games, no relation to the makers of the ST) | 675 Sycamore Dr. Milpitas, CA 95035 | The opinions expressed are my own (My lawyer isn't listening)
pardo@june.cs.washington.edu (David Keppel) (09/13/88)
>[ discussion of troolean logic ] > > AND 0 1 2 OR 0 1 2 INVERSION > ========= ========= ===== > 0 | 0 0 0 0 | 0 1 2 0 | 2 > 1 | 0 1 1 1 | 1 1 2 1 | 1 > 2 | 0 1 2 2 | 2 2 2 2 | 0 Another way to think about this is [-1,0,1]; this might give the same answers as above, although I can imagine: AND -1 0 1 OR -1 0 1 INVERSION ========= ========= ===== -1 |-1 0 0 -1 |-1-1 0 -1 | 1 0 | 0 0 0 0 |-1 0 1 0 | 0 1 | 0 0 1 1 | 0 1 1 1 |-1 ;-D on (Don't flame; I'm being provocative, not correct, today) Pardo -- pardo@cs.washington.edu {rutgers,cornell,ucsd,ubc-cs,tektronix}!uw-beaver!june!pardo
smryan@garth.UUCP (Steven Ryan) (09/13/88)
> By the way, does anyone know of a non-mechanical digital calculator or > computer that isn't essentially binary? Once upon a time there were rumours of a Russian computer with +voltage, 0 voltage, and -voltage so that it would be base 3.
ok@quintus.uucp (Richard A. O'Keefe) (09/13/88)
> By the way, does anyone know of a non-mechanical digital calculator or > computer that isn't essentially binary? Am I the only person reading this group who has heard of dekatron tubes? These were a 10-stable gadget (I think some sort of gas discharge tube). If I remember correctly they had one cathode, ten anodes, and some grids. The discharge took place between the cathode and one anode, and an electrical pulse on the grids would shift the discharge to the next or previous anode. I know that multi-digit up/down counters were built with them. I don't know if anything more complex was done, but it could have been. Since the discharge gave off visible light, you could read of the state of a dekatron counter without a separate display.
msb@sq.uucp (Mark Brader) (09/14/88)
[1] The word is "ternary", not "trinary". If you want to use the "tri-"
prefix, you have to say "triadic". Of course, as with all things in
language, this is subject to change if "trinary" becomes sufficiently
popular; the words for bases 8 and 16 both changed when they became popular
with computers. (See Knuth, volume 2, sec 4.1; in 1st edition, p. 168.)
But "ternary" is the accepted form.
[2] Please move this discussion out of comp.lang.c. Discussion of non-
binary machines should probably go in comp.arch (I'm cross-posting to
there and directing followups to it). If discussion of terminology
occurs, it should probably go to sci.lang. Sci.math is another possible
group for some aspects.
[3] While I'm posting, I may as well point out that the ENIAC calculator
(or computer, depending on your definition; it was plugboard-programmed)
of 1945 used decimal, non-BCD arithmetic, but the underlying implement-
ation was binary; each of the 10 digits in each of its 20 registers
contained 10 flip-flops each containing 2 vacuum tubes!
Mark Brader "You can't [compare] computer memory and recall
SoftQuad Inc., Toronto with human memory and recall. It's comparing
utzoo!sq!msb, msb@sq.com apples and bicycles." -- Ed Knowlesnews@ism780c.isc.com (News system) (09/14/88)
In article <6266@venera.isi.edu> lmiller@venera.isi.edu.UUCP (Larry Miller) writes: >>By the way, does anyone know of a non-mechanical digital calculator or >>computer that isn't essentially binary? > > There was also the IBM 1620, a BCD machine. Yes, decimal, but > all arithmetic was performed using table lookup, floating point ^^^ > in software, so I guess it could be called a nonbinary machine. > >Larry Miller lmiller@venera.isi.edu (no uucp) Well, actually not quite all arithmetic was by table lookup. Program counter incrementing was done with traditional bcd (i.e. binary) add logic. So I would call even this machine binary. BTW: There actually was hardware floating point. The harware supported floating precision of from 2 decimal digits to an upper bound on precision limited only by the amount of memory available to hold the data. Marv Rubinstein
phil@aimt.UUCP (Phil Gustafson) (09/14/88)
In article <3473@phri.UUCP>, roy@phri.UUCP (Roy Smith) writes: > mouse@mcgill-vision.UUCP (der Mouse) writes: > > By the way, does anyone know of a non-mechanical digital calculator or > > computer that isn't essentially binary? > > The bottom line is that digital and binary are essentially > synonymous, although I suppose in theory you could define digital as > discrete and have trinary, etc. logic. Some old (real old, 50's and 60's) counters used 10-state ring counters to hold digits. These gadgets are binary as far as logic levels go but decastable rather than bistable. They're very much analogous to wheeled mechanical calculaters. A fast (for 1967) frequency counter I worked with once had a pentastable prescalar ring. Same thing. -- Phil Gustafson, Graphics/UN*X Consultant net address above 1550 Martin Ave, San Jose, Ca 95126